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AP Physics 1 : Period and Frequency

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Example Questions

Example Question #171 : Circular, Rotational, And Harmonic Motion

A bowling ball of mass 5kg $\displaystyle 5kg$ and radius r=0.12m $\displaystyle r=0.12m$ is thrown with a rotational kinetic energy of 20J $\displaystyle 20J$ . Find its period.

Possible Answers:

0.39s $\displaystyle 0.39s$

0.90s $\displaystyle 0.90s$

0.17s $\displaystyle 0.17s$

0.52s $\displaystyle 0.52s$

0.77s $\displaystyle 0.77s$

Correct answer:

0.17s $\displaystyle 0.17s$

Explanation:

The expression for rotational kinetic energy is:

$K = \frac{1}{2}Iw^2$ $\displaystyle K = \frac{1}{2}Iw^2$

Where I is the moment of inertia for a solid sphere:

$I = \frac{2}{5}mr^2$ $\displaystyle I = \frac{2}{5}mr^2$

And w is the angular velocity:

$w = \frac{v}{r}$ $\displaystyle w = \frac{v}{r}$

Plugging these in, we get:

$K = \frac{1}{5}mv^2$ $\displaystyle K = \frac{1}{5}mv^2$

Rearranging for linear velocity:

$v=\sqrt{\frac{5K}{m}}$ $\displaystyle v=\sqrt{\frac{5K}{m}}$

The expression for period is the circumference of the ball divided by the linear velocity of the ball:

$P = \frac{c}{v}$ $\displaystyle P = \frac{c}{v}$

Plugging in expressions, we get:

$P = \frac{2\pi r}{\sqrt{\frac{5K}{m}}}$ $\displaystyle P = \frac{2\pi r}{\sqrt{\frac{5K}{m}}}$

$P = 2\pi r \sqrt{\frac{m}{5K}}$ $\displaystyle P = 2\pi r \sqrt{\frac{m}{5K}}$

We have all of these values, so time to plug and chug:

$P = 2\pi (0.12m)\sqrt{\frac{5kg}{5(20J)}}$ $\displaystyle P = 2\pi (0.12m)\sqrt{\frac{5kg}{5(20J)}}$

$\displaystyle P = 0.17s$

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Example Question #1081 : Newtonian Mechanics

A ferris wheel has a diameter of 60 meters. The carriages on the outside of the wheel are traveling at an instantaneous velocity of $3\frac{m}{s}$ $\displaystyle 3\frac{m}{s}$ . What is the period of rotation of the wheel?

Possible Answers:

$14\ \text{seconds}$ $\displaystyle 14\ \text{seconds}$

$31\ \text{seconds}$ $\displaystyle 31\ \text{seconds}$

$63\ \text{seconds}$ $\displaystyle 63\ \text{seconds}$

$81\ \text{seconds}$ $\displaystyle 81\ \text{seconds}$

$20\ \text{seconds}$ $\displaystyle 20\ \text{seconds}$

Correct answer:

$63\ \text{seconds}$ $\displaystyle 63\ \text{seconds}$

Explanation:

We can calculate the circumference of the wheel using the given radius:

$C = 2\pi r = 2\pi \cdot30 = 60\pi\ m$ $\displaystyle C = 2\pi r = 2\pi \cdot30 = 60\pi\ m$

We can use this and the given velocity to find the period:

$P = \frac{C}{v} = \frac{60\pi}{3} = 63\ \text{seconds}$ $\displaystyle P = \frac{C}{v} = \frac{60\pi}{3} = 63\ \text{seconds}$

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AP Physics 1 : Period and Frequency

Study concepts, example questions & explanations for AP Physics 1

All AP Physics 1 Resources

Example Questions

Example Question #171 : Circular, Rotational, And Harmonic Motion

Example Question #1081 : Newtonian Mechanics

All AP Physics 1 Resources

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