if the circuit has a current of 0.021a, what must the electrical potential difference across the battery be?

The speed of the banana at the equilibrium is determined as 9.9 m/s.

The speed of the banana at the equilibrium is calculated by applying the principle of conservation of mechanical energy as follows;

Kinetic energy of the banana at the lowest = Potential energy of the banana at the top height

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √ ( 2gh )

where;

The vertical height, h is calculated from the inclination of the string from the vertical.

h = L cos ( 60 )

h = 10 m x cos ( 60 )

h = 5 m

The speed of the banana at the equilibrium is calculated as follows;

v = √ ( 2 x 9.8 x 5 )

v = 9.9 m/s

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A system must meet two requirements for its momentum to be conserved: The mass of the system must remain constant during the interaction.

What is momentum?

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Four different wavelengths appear in the emission spectrum.

Since there are 3 energy levels above ground state then there are 6 possible jumps giving six wavelengths ,but because energy levels are equal jumps in different transitions the result is four different wavelengths appear.

When an electron changes from a high energy state to a lower energy one, electromagnetic radiation is released, and this electromagnetic radiation is the emission spectrum of a chemical element or chemical compound. The photon energy of the released photon is equal to the energy difference between the two states.

The distance between two wave crests, which also applies to troughs, is known as the wavelength. The number of vibrations that span a particular area in a second is known as the frequency, which is measured in cycles per second (Hz) (Hertz).

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Answer: 1a. To find the recoil velocity on the staple gun after firing the staple, we need to use the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant if no external forces act upon it.

The momentum of an object is given by the formula p = mv, where m is the mass and v is the velocity of the object.

Let's assume the mass of the staple is m_s and the velocity of the staple after being fired is v_s. The mass of the staple gun is m_g and the velocity of the staple gun after firing the staple is v_g.

According to the principle of conservation of momentum, the initial momentum of the system (before firing the staple) is zero, and the final momentum of the system (after firing the staple) is:

m_s * v_s + m_g * v_g = 0

We know the mass of the staple gun is 0.910 kg, the mass of staple is 6.8g, velocity of the staple is 1.23 m/s. So we can calculate the recoil velocity on the staple gun after firing the staple by solving the above equation:

(m_s * v_s) + (m_g * v_g) = 0

(6.8 * 10^-3 kg * 1.23 m/s) + (0.910 kg * v_g) = 0

v_g = -(6.8 * 10^-3 kg * 1.23 m/s) / 0.910 kg = -0.0075 m/s

The recoil velocity on the staple gun after firing the staple is -0.0075 m/s (negative sign indicates that the recoil velocity is in the opposite direction of the staple)

1b. The recoil velocity is so small because the mass of the staple is much smaller than the mass of the staple gun. Therefore, the staple gun will only experience a small recoil velocity due to the firing of the staple. This is because the principle of conservation of momentum states that the momentum of an object is directly proportional to its mass and velocity. In this case, the velocity of the staple is much larger than the velocity of the staple gun, but the mass of the staple is much smaller than the mass of the staple gun, which results in a small recoil velocity.

As the radius grows, the angular acceleration decreases. For there to be no slippage, the coefficient of static friction must be larger than or equal to (1/3)tan.

When an object is in static friction, the frictional force opposes the application of force, and the object stays at rest until the static friction force is removed. In kinetic friction, the frictional force opposes the motion of an item. On the other hand, static friction happens when two surfaces are at rest with respect to one another. Between zero and the force needed to start motion, static friction varies. The force needed to start a motion or displace static friction keeps getting stronger. Physicists use the newton, an International System (SI) unit, to measure force.

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The third charge q should be placed in between +Q and +4Q so that all three charges will be in equilibrium. Hence, the sign and magnitude of third charge is -4Q/9 and position is d/3 distance from +Q.

Coulomb's law asserts that the force of attraction or repulsion between two charged bodies is proportional to the inverse square distance between them and directly proportional to the product of their charges.

Coulomb's Law; F = Kq1q2/r2;

Net force = 0 (since, all three are in equilibrium )

       KQq/x^2 = Kx4Qxq/(d-x)^2

   1/x^2 = 4/(d-x)^2

=> 1/x = 2/(d-x)

=> x=> d/3

KQx4Q/(d)^2 + Kx4Qxq/(d-x)^2 = 0 (since, all three are in equilibrium);

      => Q/(d)^2 = - q/(d-d/3)^2

=>  Q/(d)^2 = -q x 9/ 4xd^2

=> q= - 4Q/9

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Answer:

350 N [Forward]

Explanation:

Recall the equation for force

Force (N) = mass (kg) * acceleration (m/s²)

or

F = ma

You're given the mass of the stretcher and lion combined is 175kg. Because the lion is in the stretcher, we treat can treat them as one body.

m = 175 kg

You also know the stretcher and lion body is accelerating at 2 m/s².

You have all the information needed to solve.

F = ma

= (175 kg)(2 m/s²)

= 350 N

Because Force is a vector quantity, you have to say the direction. The direction is simply "forward" so make sure to write forward to complete your answer like:

350 N [Forward]

The net force F4 exerted on the runner in lane 4 will be 2 times the net force F1 exerted on the runner in lane 1.

What is newton's second law?

Newton's second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This claim is correct because Newton's Second Law states that the net force on an object is equal to the mass times the acceleration of the object.

Therefore, since the runners have the same mass, the acceleration of the runner in lane 4 must be twice that of the runner in lane 1 to account for the difference in speed.

Since acceleration is directly proportional to the net force on an object, this implies that the net force F4 exerted on the runner in lane 4 is twice the net force F1 exerted on the runner in lane 1.

Therefore, The net force F4 exerted on the runner in lane 4 will be 2 times the net force F1 exerted on the runner in lane 1.

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The work done on the shuttle will be negative, if its changes its circular orbit to a lower altitude.

The gravitational force between the object and the earth is balanced by the centrifugal force acting on the object during the circular motion. If a satellite of mass m, orbits around the earth in a circular path of radius R, then centrifugal force will be, mv²/R.

if the mass of the earth is M, and universal gravitational constant is G, then gravitational force between the earth and the satellite would be GMm/R².

mv²/R = GMm/R²

mv² = GMm/R

0.5mv² = 0.5GMm/R

But 0.5mv² = K = Kinetic energy of the satellite

K = 0.5GMm/R

So lesser the radius of the orbit, more the kinetic energy will be required for the satellite to orbit around the earth. So the work will be done by the orbit, in other words the work done on the satellite will be negative because it is done by the satellite.

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The mass of the Martian atmosphere is approximately 1.04*10^15 kg. This means that the Martian atmosphere has a mass of around 1.04 trillion kilograms.

The data from SAM corroborated the composition of the atmosphere on Mars' surface: 95% by volume of carbon dioxide (CO2), 2.6% of molecular nitrogen (N2), 1.9% of argon (Ar), 0.16% of molecular oxygen (O2), and 0.06% of carbon monoxide (CO).

The mass of the Martian atmosphere can be calculated using the Ideal Gas Law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

To calculate the mass of the atmosphere, we can assume that the temperature is constant and that the atmosphere is at sea level, so we can approximate the volume as the volume of a sphere with a radius of 3396.2 km. The volume of a sphere is 4/3πr^3.

The number of moles can be calculated from the pressure and the volume using the Ideal Gas Law: n = PV/RT.

Once we have the number of moles, we can use the molar mass of the atmosphere to find the mass of the atmosphere.

The calculation for the mass of the Martian atmosphere is as follows:

mass = (4/3)π(3396.210^3)^30.62/(8.314*(273+(-20)))

mass = 1.04*10^15 kg approximately

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Some situations where charges occur naturally are lightning during thunderstorms.

There are two kinds of electric charge: positive and negative (commonly conveyed by protons and electrons individually). Examples of the types of charges are subatomic flecks or the particles of matter: Protons are positively charged. Electrons are negatively charged. Neutrons have naught charges.

Due to the apparent additional nature of the charge, the total electric charge of such a structure would be equal to the algebraic summation of the electric charges present all around the structure or system. The rule of superimposition of electric charge explains the compelling nature of the charge.

So we can conclude that Charging by Friction​​ When two things are rubbed against each other

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Lightning, Friction,Electrostatic Induction, Piezoelectricity, Thermoelectricity, Photoelectric effect and Cosmic ray

Lightning: During a thunderstorm, charges can build up in the atmosphere due to the movement of water droplets and ice particles. This can result in a lightning strike, which is a discharge of electricity through the atmosphere.

Friction: When two materials rub against each other, electrons can be transferred from one material to the other, resulting in a separation of charges. This is known as the triboelectric effect.

Electrostatic Induction: Electric charges can be induced on an object by bringing it near a charged object without making contact.

Piezoelectricity: Certain materials, such as quartz crystals, can generate a voltage when they are under mechanical stress, resulting in the separation of charges.

Thermoelectricity: A temperature difference between two materials can cause a flow of charge carriers, resulting in a voltage difference between the two materials.

Photoelectric effect: When light hit a metal surface , electrons are emitted from the surface and produces charge.

Cosmic ray: Cosmic rays are high-energy particles that come from outer space, which can ionize atoms and molecules in the atmosphere, resulting in the separation of charges.

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A car of mass m is on a road tilted at an angle θ. The correct expression for the normal force is: N = mg cos  θ

The free-body diagram is depicted on the attached picture. The forces acted on the car are: gravitational force (the weight of the car), normal force, and friction (if any).

Weight is equal to mass times the acceleration due to gravity.

w = mg

Where:

m = mass of the car

g = acceleration due to gravity

Since the road is tilted, the weight force can be written as its x-component and y-component:

wx = mg sin  θ

wy = mg cos  θ

Normal force is always perpendicular to the surface. Since the car moves at x -axis, it means that the net force at y-axis is zero.

Refer to the attached picture:

∑Fy = 0

N -  mg cos  θ = 0

N = mg cos  θ

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A beam of microwave having a frequency of 1.0 times 109hz will have a longer wavelength.

Microwaves and radar are two types of electromagnetic radiation that are used in a variety of applications. The frequency of a microwave is 1.0 times 109hz, while the frequency of a radar beam is 5.0 times 1011th hz.

When comparing the two, the radar beam has a much higher frequency, but the microwave has the longer wave length.

To calculate this, we can use the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. Using this equation, we can calculate that the wavelength of the microwave is 3.00 x 10-2 meters, while the wavelength of the radar beam is 6.00 x 10-3 meters. Therefore, the microwave has the longer wave length.

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A proton (with a rest mass m = 1.67×10⁻²⁷kg) has a total energy that is 4.00 times its rest energy then the kinetic energy Ek of the proton is 2.818GeV.

The power an object has as a result of motion is referred to as kinetic energy. In order to accelerate an object, a force must be applied. Applying force requires effort on our part. Following completion of the work, energy is transferred to the object, which then moves at a new, constant speed.

Given that

A proton with a rest mass m = 1.67×10⁻²⁷kg

A total of 4.00 times its rest energy.

Now the total energy Etotal = KE + mc²

KE = E - mc²

Then E = 4mc²

Therefore KE = 3mc²

KE = 3×(1.67×10−27kg)(3×10⁸m/s)²

KE = 45.09×10⁻¹¹J

We know that 1eV =1.6×10⁻¹⁹J

Then KE =28.18×10⁸eV = 2.818GeV.

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The fluid pressure at the bottom of the box is determined by the weight of the fluid above it, which is determined by the height of the fluid column.

When the box is oriented with the shortest side at the bottom, the height of the fluid column is at its maximum, and thus the weight of the fluid above the bottom of the box is at its maximum.

This results in the greatest force being exerted on the bottom of the box, and thus the greatest fluid pressure at the bottom.

When the box is oriented with the taller side at the bottom, the height of the fluid column is shorter, resulting in less weight of the fluid above the bottom of the box, and thus less force being exerted on the bottom of the box and less fluid pressure at the bottom.

It's also important to note that the weight of the fluid is directly proportional to the volume of fluid which means the pressure at the bottom will also be greatest when the volume of fluid is at its maximum, which is when the box is oriented with the shortest side at the bottom.

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Correct option is B, explosion of the primer mix explosion of the primer mix  causes a bullet or projectile to travel down the barrel of a firearm and exit at the muzzle.

An object that is propelled by the application of an external force and then moves freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and warfare, despite the fact that any item traveling through space is a projectile.

Projectile motion has many uses in both physics and engineering. Examples include the motion of any ball in sports, fireworks, and meteors entering the Earth's atmosphere. These things are known as projectiles, and the path they take is known as a trajectory.

An item or particle that is propelled into a gravitational field, such as from the surface of the Earth, and moves along a curved route only under the influence of gravity is said to be experiencing projectile motion.

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There is no relationship between the wave speed and the wave frequency.

Let us note that the term wave would have to do with the kind of disturbance that is taking place in a medium and would lead to the transfer of energy. We should know that when a wave is in motion, the movement of the wave would have to be described in terms of about three main parameters and these are;

The wave frequency would have to do with the way that the number of cycles that the wave is able to complete per second and this is connected to the period of the wave.

However, the frequency of the wave is not affected by the speed of the wave as the both are independent of each other as seen in the description above.

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If you were trying to build a soundproof room, the material that would absorb the most sound, based on the coefficient of absorption for each material, would be heavy curtains.

What do you mean by coefficient of absorption?

The coefficient of absorption is a measure of how well a material absorbs sound. It is a dimensionless number, usually expressed as a decimal between 0 and 1, with a higher value indicating better sound absorption. The coefficient of absorption is used to determine the sound absorption properties of a material in a specific frequency range, and it is usually determined by measuring the sound energy absorbed by a material as compared to the sound energy that is incident upon it.

It is usually expressed as a decimal between 0 and 1, with a higher value indicating better sound absorption.

According to the data available, heavy curtains have a higher coefficient of absorption than carpet, clay tile, and wood. They are typically made of thick, dense fabrics that are able to absorb a significant amount of sound energy, which helps to reduce noise transmission through walls and ceilings. Carpet, clay tile and wood have lower coefficient of absorption values, which means they are not as good at absorbing sound.

It's worth noting that soundproofing a room is a complex task that involves multiple aspects, not only the absorption of sound, but also its insulation and soundproofing. So, it's always better to consult with a professional to get the best result.

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a) The time of revolution is 97.57 minute.

b) The acceleration of gravity at the orbit is 8.10 m/s².

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.

Orbital speed of the satellite is = 425 km/min.

a) The time of revolution = perimeter of the orbit ÷ orbital speed of the satellite

= 2π × 6600 km/425 km/min

= 97.57 minute.

b) The acceleration of gravity at the orbit is = g (R/r)²

= 9.8 × (6000/6600)² m/s²

= 8.10 m/s²

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where y represents how far below point A in the vertical plane point B is. We determined that this distance's magnitude was 26.5m in portion (a). It is a negative number now that it is less than the zero reference level.

Potential energy is a form of energy that is stored but is dependent on the relative positions of different system components. Stretching or compressing a spring increases its potential energy. A steel ball has far more potential energy when it is raised above the surface of the earth than when it is brought to Earth.

What does potential energy mean? Potential energy is the energy that is conserved or stored in a substance or an item. The object or substance's position, organization, or state determines the amount of stored energy. Consider it as energy with the "potential" to do work.

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If a mass of 40.0 n is postponed from a spring that has a force constant of 200 n/m. then maximum value of the force is 317.94 N

A force is an effect with the ability to change a motion of an object. An massed object can change its velocity, or accelerate, as a result of a force.

According to the given question

weight of the object w=40 N

hence mass will be m=w/g = 40/9.81

spring constant k= 200 N/m

frequency f=10 Hz

anplitude generated A=2cm= 2*10^-2m

As the system is undamped equation for amplitude can be

simplified as

A= F/m[(w^2-Wo^2)^2+(bW/m)^2]^1/2 here b=0

so,

A= F/m(w^2-wo^2)

hence force is F=Am(w^2-wo^2)

F=0.02*(40/9.81)[(2

10)^2 -(200/40)*9.81 ]

= 317.94 N

hence maximum value of force is F= 317.94 N

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The pressure will be the same if each of these boxes have the same elevation. On the second box, the air's overall force will be greater.

Although I'm sure some academics would be furious about this, it helps me to conceive of air as water. However, as air is a considerably lighter fluid than water, this replacement is acceptable. Because there is the same quantity of water on each submarine, the pressures will be the same if there are two of them at the ocean's bottom. But a larger sub will be subjected to more force, which increases the likelihood of it bowing. I would take into consideration the units of pressure and force per unit area as the force idea is difficult to express.

Since we are aware that pressure is constant, we may set them equal by using the formulas P1=P2 and P1=F1/A1 and P2=F2/2(A1).

F1/A1=F2/2A1

It is evident that F2=2F1.

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The change in momentum of the 1000kg of water is zero, in other words, the momentum before and after the bend is the same.

The change in momentum (Δp) of an object is the final momentum (pf) minus the initial momentum (pi). Since the mass is constant and the direction of the velocity is changed by 90 degrees, the magnitude of the change in momentum can be calculated as:

Δp = m × (vf - vi) = 1000 kg × (1.4 m/s - 1.4 m/s) = 0 kg-m/s

The direction of the change in momentum is perpendicular to the direction of velocity change, in this case, it's in the vertical direction.

So, the change in momentum of the 1000kg of water is zero, in other words, the momentum before and after the bend is the same.

This means that no force is required to change the direction of the water, but the pipe needs the thrust block to hold it in place since the force of the water moving at high velocity could cause the pipe to move or even break.

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The complete question is as follows:

For part A. The impulse of the force is the area under the force-time graph. The figure you provided is not accessible to me, but if the graph is of a constant force over time, the impulse can be calculated as:

[tex]Impulse = force x time = (40 N) (20 s) = 800 N*s[/tex]

For part B. The average force exerted on the particle is the impulse divided by the time, it can be calculated as:

[tex]Average force = impulse / time = 800 N*s / 20 s = 40 N[/tex]

Momentum is a concept in physics that describes the tendency of an object to continue moving in the same direction at the same speed. It is a vector quantity, meaning it has both a magnitude and a direction. The momentum of an object is equal to its mass multiplied by its velocity.

In the context of finance, momentum refers to the rate of acceleration of price or volume changes in a security or market. It is often used by investors to identify trends and make investment decisions.

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The given statement, lightning protection is achieved by providing an elevated well-grounded conductor that will more likely launch the upward-going discharge that connects with the downward moving leader, thereby providing a path to ground for the lightning current that does not go through the object to be protected, is true.

Lightning protection is a system designed to protect a structure or facility from damage caused by a lightning strike. This is typically achieved by providing a path for the lightning current to safely pass through the structure and into the ground, rather than allowing it to damage or destroy the building or its contents. One common method for achieving lightning protection is by installing an elevated, well-grounded conductor, such as a lightning rod, that will more likely launch the upward-going discharge that connects with the downward moving leader, providing a path to ground for the lightning current. This prevents the current from passing through the protected structure and reduces the risk of damage. Other methods such as lightning arrestors, surge protection devices and earthing are also used as a part of lightning protection system.

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Immediately after time t = 0, the positive and negative charges attract each other, so they stay in the capacitor. Current flows clockwise through the circuit.

The capacitor plates' charges have been divided after time t=0, leaving one plate with a positive charge and the other with a negative charge. The attractive force between the positive and negative charges will now cause the charges on the plates to remain in place. In the circuit, current also moves in a clockwise direction. This is due to the fact that the positive charges will travel toward the positive plate, and the negative charges will move toward the negative plate, causing a current to flow clockwise through the circuit.

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Answer: 150 j

Explanation:

3x5x10=150 j

gravity equals 10

Answer:

[tex]10500\; {\rm N}[/tex], assuming that the motion is at constant speed.

Explanation:

To find the work that was done, multiply power by time:

[tex]\begin{aligned}(\text{work}) &= (\text{power})\, (\text{time}) \\ &= (3500\; {\rm W}) \, (3\; {\rm s}) \\ &= 10500\; {\rm J}\end{aligned}[/tex].

Assume that the computer was lifted at a constant speed. The force that lifted the computer would be constant and equal to opposite of the weight of the computer.

Since force is constant, divide work by displacement to find this force:

[tex]\begin{aligned}(\text{force}) &= \frac{(\text{work})}{(\text{displacement})} \\ &= \frac{10500\; {\rm J}}{1\; {\rm m}} = 10500\; {\rm N}\end{aligned}[/tex].

In other words, the magnitude of the force that lifted the computer is [tex]10500\; {\rm N}[/tex]. Under the assumption that the computer was lifted at constant velocity, the weight of the computer would have the same magnitude, [tex]10500\; {\rm N}\![/tex].

The capacitor can carry 6.6 × 10⁻³ F charge, if the parallel plate capacitor with C=2.2μF and plate separation is 1 mm.

Electric potential difference across cap. plates and E field inside related by separation d. Maximum allowed field before breakdown then implies maximum voltage for given d.

Let the critical field, E₁ = 3 × 10⁶ v/m

Separation between the plates, d = 1 mm = 1 × 10⁻³ m

The breakdown voltage, V₁ = E₁ × d

V₁ = 3 × 10⁶ × 1 × 10⁻³ = 3 × 10³ V

Charge carry by the capacitor during breakdown, Q = C × V₁

Q = 2.2 × 10⁻⁶ × 3 × 10³

Q = 6.6 × 10⁻³ F

--The give question is incomplete, the complete question is,

"How much charge a parallel plate capacitor with C=2.2μF, and separation of plate 1 mm, can carry before the dielectric breakdown. If the critical field is, E₁ = 3 × 10⁶ v/m.

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You wish to reduce the stress of some vehicle that should move at some velocity v, and as want to know what tires would be better (i.e., have less centripetal force). we can write the centripetal force as)

= F = m* v^2 / r

This gives the force on a point mass m moving in a circle with radius r with the velocity v. randomly the (absolute value of the) velocity of the point throughout the circle is the similar as the velocity of your vehicle.

Hence, if you decide to hold the speed constant and reduce the centripetal force, this says you to expand the diameter of the tires.

Now what about the second equation:

F = m* r* w^2

F, m and r are the similar as above, but w (even the small Greek letter omega) is the angular velocity. It says you how much time it needs for the wheel to turn by a definite angle.

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