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AP Physics 1 : Circular, Rotational, and Harmonic Motion

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Example Questions

Example Question #2 : Angular Velocity And Acceleration

If it takes a bike wheel 3 seconds to complete one revolution, what is the wheel's angular velocity?

Possible Answers:

$2.09s^{-1}$

$0.84s^{-1}$

$3.37s^{-1}$

$1.28s^{-1}$

Correct answer:

$2.09s^{-1}$

Explanation:

The definition of angular velocity is $\omega=\frac{\Delta \Theta }{\Delta t}$ .

By identifying the given information to be $\Delta \Theta =2\pi$ and $\Delta t =3s$ , we can plug this into the equation to calculate the angular velocity:

$\omega=\frac{2\pi}{3 s}=2.09s^-1$

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Example Question #1 : Circular And Rotational Motion

What is the angular velocity of the second hand of a clock?

Possible Answers:

$\frac{\pi rad}{30s}$

$\frac{\pi rad}{60s}$

$\frac{2\pi rad}{s}$

$\frac{60 rad}{\pi s}$

$\frac{30 rad}{\pi s}$

Correct answer:

$\frac{\pi rad}{30s}$

Explanation:

The angular velocity of the second hand of a clock can be found by dividing the number of radians the second hand will travel over a known period of time. Thankfully for a clock, we know that the second hand will make one revolution, i.e. covering $2\pi rad$ in one minute, or 60s. The formula for angular velocity is:

$\omega = \frac{\theta}{t}$

So the angular velocity, $\omega$ is $\frac{2\pi rad}{60s}$ , which simplifies to our answer, $\frac{\pi rad}{30s}$

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Example Question #1 : Circular And Rotational Motion

What is the difference in the angular velocity of the second hand of radius 1cm on a wristwatch, compared to the second hand of radius 5m on a large clock tower?

Possible Answers:

The clocktower second hand has an angular velocity that is 5 times faster than that of the wristwatch

The clocktower second hand has an angular velocity that is 500 times faster than that of the wristwatch

No difference

The clocktower second hand has an angular velocity that is 20 times faster than that of the wristwatch

The clocktower second hand has an angular velocity that is 500 times slower than that of the wristwatch

Correct answer:

No difference

Explanation:

The angular velocity should not change based on the radius of the second hand. No matter what size the second hand, it will still cover one revolution every minute or 60s. The linear velocity will be greater and the angular momentum will also be greater for the clocktower, but its angular velocity will be the same. This can be seen by looking at the equation for angular velocity:

$\omega=\frac{\theta}{t}$

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Example Question #1 : Angular Velocity And Acceleration

A ferris wheel has a trip length of 3min, that is it takes three minutes for it to make one complete revolution. What is the angular velocity of the ferris wheel if it only takes passengers around one time, in $\frac{rad}{s}$ ?

Possible Answers:

18.85

0.35

0.035

2.094

Correct answer:

0.035

Explanation:

Angular velocity, in $\frac{rad}{s}$ , is given by the length traveled divided by the time taken to travel the length:

$\omega=\frac{\theta}{t}$

We are told that the amount of time taken to make one revolution is 3min. One revolution is equal to $2\pi\ rad$ , and 3 minutes is equal to 180 seconds. Divide the radian value by the seconds value to get the angular velocity.

$\omega =\frac{2\pi}{180}$

$\omega=0.035\frac{rad}{s}$

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Example Question #1 : Circular And Rotational Motion

A wheel makes one full revolution every seconds and has a radius of . Determine its angular velocity .

Possible Answers:

$w=\pi \frac{rads}{s}$

$w=10\pi \frac{rads}{s}$

$w=5\pi \frac{rads}{s}$

$w=\frac{\pi}{5} \frac{rads}{s}$

Correct answer:

$w=\pi \frac{rads}{s}$

Explanation:

For this question, the angular velocity can be given by the equation:

$w=\frac{\theta}{t}$ , where $\theta$ is the angle made and is the time taken to make this angle.

In this problem, the wheel makes one full revolution( $\theta=2\pi$ ) in seconds.

Therefore:

$w=\frac{2\pi}{2s}=\pi \frac{rads}{s}$

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Example Question #1 : Circular And Rotational Motion

A CD rotates at a rate of $5\frac{rad}{s}$ in the positive counter clockwise direction. After pressing play, the disk is speeding up at a rate of $2\frac{rad}{s^2}$ . What is the angular velocity of the CD in $\frac{rad}{s}$ after 4 seconds?

Possible Answers:

$6 \frac{rad}{s}$

$19.5 \frac{rad}{s}$

$10 \frac{rad}{s}$

$13 \frac{rad}{s}$

$6.5 \frac{rad}{s}$

Correct answer:

$13 \frac{rad}{s}$

Explanation:

Given initial angular velocity, angular acceleration, and time we can easily solve for final angular velocity with:

$\omega=\omega _{0}+\alpha t$

$\omega=5\frac{rad}{s}+2\frac{rad}{s} (4)={13\frac{rad}{s}}$

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Example Question #1001 : Ap Physics 1

If a ferris wheel has height of 100m, find the angular velocity in rotations per minute if the riders in the carts are going $7\frac{m}{s}$ .

Possible Answers:

$7.77\frac{rotations}{minute}$

$1.34 \frac{rotations}{minute}$

$1.94 \frac{rotations}{minute}$

$3.95 \frac{rotations}{minute}$

None of these

Correct answer:

$1.34 \frac{rotations}{minute}$

Explanation:

If the ferris wheel has height 100m then it must have radius 50m .

The circumference of the ferris wheel, or the distance of one rotation, is then:

$2\pi*r=C$

$2\pi*50m=C$

$2\pi*50m\approx 314m$

Convert the given velocity into meters per minute, or $\frac{m}{min}$ :

$7\frac{m}{s}*\frac{60 s}{1 min}=420\frac{m}{min}$

Find rotations per minute:

$420\frac{m}{min}*\frac{1 rotation}{314m}=\frac{1.34 rotations}{minute}$

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Example Question #1 : Angular Velocity And Acceleration

A person of mass 95kg is riding a ferris wheel of radius 10m . The wheel is spinning at a constant angular velocity of 1rpm . Determine the linear velocity of the rider.

Possible Answers:

$\frac{1.05 meters}{second}$

$\frac{4.25 meters}{second}$

$\frac{3.25 meters}{second}$

$\frac{.86 meters}{second}$

$\frac{2.65 meters}{second}$

Correct answer:

$\frac{1.05 meters}{second}$

Explanation:

Convert $\frac{rotations}{minute}$ to $\frac{meters}{second}$ :

$1\frac{rotation}{minute}*\frac{1 minute}{60 seconds}*\frac{2*pi*10meters}{1 rotation}=\frac{1.05 meters}{second}$

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Example Question #11 : Angular Velocity And Acceleration

Radius of the earth: $6.37*10^{6}m$

A train is traveling directly north at $110\frac{km}{hr}$ . Estimate its angular velocity with respect to the center of the earth.

Possible Answers:

$7.8*10^{-6} \frac{radians}{second}$

$9.1*10^{-6} \frac{radians}{second}$

$6.2*10^{-6} \frac{radians}{second}$

$4.8*10^{-6} \frac{radians}{second}$

$2.5*10^{-6} \frac{radians}{second}$

Correct answer:

$4.8*10^{-6} \frac{radians}{second}$

Explanation:

Convert $\frac{km}{hr}$ to $\frac{m}{s}$

$110\frac{km}{hr}*\frac{1hr}{3600 seconds}*\frac{1000m}{1km}=30.6\frac{m}{s}$

Use the following relationship and plug in known values:

$\omega=\frac{v}{r}$

$\omega=\frac{30.6}{6.37*10^6}$

$\omega=4.8*10^{-6} \frac{radians}{second}$

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Example Question #12 : Circular And Rotational Motion

$1 \ \text{day on Pluto}=6.39 \ \text{days on Earth}$

Pluto radius: 1.186*10^6 m

Determine the linear velocity of someone standing on the surface of Pluto due to the rotation of the planet.

Possible Answers:

$13.5\frac{m}{s}$

$15.7\frac{m}{s}$

$2.5\frac{m}{s}$

$9.3\frac{m}{s}$

$4.3\frac{m}{s}$

Correct answer:

$13.5\frac{m}{s}$

Explanation:

Convert units of time into radians per second:

$\frac{2\pi~radians}{1~pluto~day}*\frac{1~pluto~day}{6.39~earth~days}*\frac{1 earth~ day}{24 hours}*\frac{1 hour}{3600 seconds}=\frac{1.138*10^{-5}radians}{sec}$

Convert to linear distance:

$\frac{1.138*10^{-5}radians}{second}*\frac{1.186*10^6meters}{1 radian}={13.5\frac{m}{s}}$

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AP Physics 1 : Circular, Rotational, and Harmonic Motion

Study concepts, example questions & explanations for AP Physics 1

All AP Physics 1 Resources

Example Questions

Example Question #2 : Angular Velocity And Acceleration

Example Question #1 : Circular And Rotational Motion

Example Question #1 : Circular And Rotational Motion

Example Question #1 : Angular Velocity And Acceleration

Example Question #1 : Circular And Rotational Motion

Example Question #1 : Circular And Rotational Motion

Example Question #1001 : Ap Physics 1

Example Question #1 : Angular Velocity And Acceleration

Example Question #11 : Angular Velocity And Acceleration

Example Question #12 : Circular And Rotational Motion

All AP Physics 1 Resources

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