AP Physics 1 : Circular and Rotational Motion

Study concepts, example questions & explanations for AP Physics 1

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Example Questions

Example Question #101 : Circular, Rotational, And Harmonic Motion

A person of mass is riding a ferris wheel of radius . The wheel is spinning at a constant angular velocity of . Determine the force exerted on the rider by their seat at the top of the ferris wheel.

Possible Answers:

None of these

Correct answer:

Explanation:

Convert  to :

Definition of centripetal acceleration:

Plug in values:

Superposition of forces:

Where both and are pointing down, and thus negative.

Solve for

Plug in values:

Example Question #102 : Circular, Rotational, And Harmonic Motion

A person of mass is riding a ferris wheel of radius . The wheel is spinning at a constant angular velocity of . Determine the force exerted on the rider by their seat at the bottom of the ferris wheel.

Possible Answers:

Correct answer:

Explanation:

Convert  to :

Definition of centripetal acceleration:

Plug in values:

Superposition of forces:

Where is pointing down, and thus negative. However, is pointing up, and thus positive.

Solve for

Plug in values:

Example Question #1011 : Newtonian Mechanics

Radius of earth:

Estimate a centripetal acceleration of someone standing on the equator with respect to the center of the earth.

Possible Answers:

None of these

Correct answer:

Explanation:

A person on the equator travels in a circle with the same radius as the earth's every .

Thus, distance divided by time:

Convert  to and plug in values:

Use the definition of centripetal acceleration:

Plug in values:

Example Question #1012 : Newtonian Mechanics

Earth mass:

Earth distance from the Sun:

Velocity of the Earth: 

Estimate the centripetal acceleration of the earth in relation to the sun.

Possible Answers:

Correct answer:

Explanation:

The velocity of the earth is

Convert to

Plug in values:

Example Question #21 : Centripetal Force And Acceleration

Estimate the centripetal acceleration of a car driving  around a  long perfectly circular track.

Possible Answers:

Correct answer:

Explanation:

Convert  to

Convert  to :

Use the equation for centripetal acceleration:

Example Question #22 : Centripetal Force And Acceleration

Pluto distance to sun:

Determine the centripetal acceleration of Pluto with respect to the Sun.

Possible Answers:

Correct answer:

Explanation:

Combine equations:

Convert to meters and seconds and plug in values:

Example Question #31 : Centripetal Force And Acceleration

A car of mass goes in a circle of radius at a velocity of . Calculate the centripetal force a driver of mass would experience in the car.

Possible Answers:

Correct answer:

Explanation:

First, convert units of the magnitude of velocity (speed):

Convert to meters and plug in values:

Example Question #61 : Circular And Rotational Motion

Consider the following system:

 

Spinning rod with masses at end

Two spherical masses, A and B, are attached to the end of a rigid rod with length l. The rod is attached to a fixed point, p, which is at a height, h, above the ground. The rod spins around the fixed point in a vertical circle that is traced in grey.  is the angle at which the rod makes with the horizontal at any given time ( in the figure).

If the masses are traveling at a velocity of  as they mass through the horizontal, what is the greatest centripetal force felt by mass B? Neglect air resistance and internal friction forces.

Possible Answers:

Correct answer:

Explanation:

Before we even begin thinking about what sort of equations we will be using, we first need to determine at which point mass B is feeling its greatest centripetal force. This will be whenever the mass is traveling at its fastest. Thinking about the law of conservation of energy, the mass will be traveling at its fastest when the potential energy of the system is minimized. There are two different masses in the system that are linked. Therefore, potential energy will be minimized when the larger mass is at its lowest point. This is when the rod is vertical and mass A is at the bottom. Now we can move on, beginning with the expression for centripetal force:

The only value we don't know is velocity. However, we can find it by using the expression for conservation of energy:

If we assume that point p is at a height of 0, we can eliminate initial potential energy to get equation (1):

Now let's expand each term moving from left to right:

Since the velocities of both masses are the same, we can say:

Moving onto final potential:

The final position of the rod is vertical with mass A at the bottom (which is a half length of rod below our reference point) and mass B at the top (half length rod above), so we can rewrite 

Moving on to final kinetic:

Substituting these into equation (1) we get:

To make things look nicer, lets eliminate the fraction from each term:

We are solving for final velocity, so let's begin rearranging:

Note how the masses were switched in the final term since it switched sides. No some more rearranging:

We know all of those values, so time to plug and chug:

Now we go back to our expression for centripetal force:

We need to determine r, which is simply half the length of the rod:

Now that we know all of our values, we can solve the problem:

Example Question #33 : Centripetal Force And Acceleration

Consider the following system:

 

Spinning rod with masses at end

Two spherical masses, A and B, are attached to the end of a rigid rod with length l. The rod is attached to a fixed point, p, which is at a height, h, above the ground. The rod spins around the fixed point in a vertical circle that is traced in grey.  is the angle at which the rod makes with the horizontal at any given time ( in the figure).

If the maximum centripetal force felt by mass A is , what is the minimum centripetal force it feels? Neglect air resistance and internal friction.

Possible Answers:

Correct answer:

Explanation:

First we need to determine when at which points mass A will be experiencing the most/least centripetal force. The most will be when the rod is vertical and mass A is at the bottom (initial condition). This is because the potential energy is minimized (thus kinetic is maximized) when the large mass is at its low point. Therefore, the lest centripetal force will be when mass A is at the top (final condition). So now let's begin with the equation for conservation of energy:

Unfortunately we can't eliminate any terms, so let's begin expanding them one at a time:

If we assume that the lowest point of the circle has a height of 0, the initial potential energy of mass A will be 0:

We also know that the height at the top of the circle is exactly one rod length from our reference height, so we can say:

Moving on to initial kinetic:

Since bot velocities are always the same, we can say:

Now final kinetic. We'll just skip ahead to it's final form:

Note how it's the same as before, except that the masses are switched. No final kinetic. We'll skip to it's final form again:

Now plugging all of these back into the expression for conservation of energy, we get:

In order to find the final centripetal force, we are going to need to need the final velocity, so let's begin rearranging for that:

Factoring and dividing, we get:

We know every variable except initial velocity, which we can solve for by using the equation for centripetal force:

Where mass is mass B, v is the initial velocity, and radius is half the length of the rod:

Now we rearrange for initial velocity:

Plugging this back into our big equation along with the rest of the variable:

 

Now using the expression for centripetal force to find our final answer:

Example Question #31 : Centripetal Force And Acceleration

The radius of earth is . Assume the Earth is perfectly spherical.

A space shuttle has a mass of approximately 2.04 million kilograms when ready for launch.  What is the difference of the force needed to create liftoff if the shuttle were launched from the equator versus the North Pole (due to the rotation of the Earth)? 

Possible Answers:

It would need  less to liftoff.

It would need  less to liftoff.

It would need  less to liftoff.

It would need the same upward force to liftoff.

It would need  less to liftoff.

Correct answer:

It would need  less to liftoff.

Explanation:

To find the difference in force upwards for liftoff, we need to find how much centrifugal force is generated from the rotation of the Earth.  The equation for centrifugal force is:

Where  is the mass of the object,  is the distance from the center of rotation the object is, and ,  being the period of the rotation.  We know that the earth rotates once per day, so we can find the period of rotation in seconds:

Now we solve for the centrifugal force:

This is all we need to calculate, because we know that the force pulling the shuttle down due to gravity would be identical from the equator to the North Pole on our idealized spherical Earth.

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