AP Physics 1 : Period and Frequency

Study concepts, example questions & explanations for AP Physics 1

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Example Questions

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

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

Possible Answers:

\(\displaystyle 0.39s\)

\(\displaystyle 0.90s\)

\(\displaystyle 0.17s\)

\(\displaystyle 0.52s\)

\(\displaystyle 0.77s\)

Correct answer:

\(\displaystyle 0.17s\)

Explanation:

The expression for rotational kinetic energy is:

\(\displaystyle K = \frac{1}{2}Iw^2\)

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

\(\displaystyle I = \frac{2}{5}mr^2\)

And w is the angular velocity:

\(\displaystyle w = \frac{v}{r}\)

Plugging these in, we get:

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

Rearranging for linear velocity:

\(\displaystyle v=\sqrt{\frac{5K}{m}}\)

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

\(\displaystyle P = \frac{c}{v}\)

Plugging in expressions, we get:

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

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

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

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

\(\displaystyle P = 0.17s\)

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 \(\displaystyle 3\frac{m}{s}\). What is the period of rotation of the wheel?

Possible Answers:

\(\displaystyle 81\ \text{seconds}\)

\(\displaystyle 14\ \text{seconds}\)

\(\displaystyle 63\ \text{seconds}\)

\(\displaystyle 20\ \text{seconds}\)

\(\displaystyle 31\ \text{seconds}\)

Correct answer:

\(\displaystyle 63\ \text{seconds}\)

Explanation:

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

\(\displaystyle C = 2\pi r = 2\pi \cdot30 = 60\pi\ m\)

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

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

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