A computer hard disk starts from rest, then speeds up with an angular acceleration of $\alpha=190 \dfrac{\text{rad}}{\text{s}^2}$ until it reaches its final angular speed of $\omega_f=7200~\text{rpm}$. How many revolutions has the disk made $t=10.0~\text{s}$ after it starts up?

Figure below shows the angular position of a potter's wheel. What is the angular displacement of that wheel between $t=5\text{ s}$ and $t=15\text{ s}$?

To throw a discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant angular acceleration, releasing the discuss after making one complete revolution. The diameter of the circle in which the discus moves is about 1.8 m. If the thrower takes 1.0 s to complete one revolution, starting from rest, what will be the speed of the discus at release?

A turntable rotates counterclockwise at 78 rpm. A speck of dust on the turntable is at $\theta = 0.45 \text { rad at } t = 0 \mathrm { s }$. What is the angle of the speck at t = 8.0 s? Your answer should be between 0 and $2 \pi \mathrm { rad }$.

The big claw-snapping shrimp is aptly named-it has one big claw that snaps shut with remarkable speed. The part of the claw that moves rotates through a $90^{\circ}$ angle in $1.3 \mathrm{~ms}$. If we assume that the claw is $1.5 \mathrm{~cm}$ long and that it undergoes a constant angular acceleration:
a. What is the angular acceleration in $\mathrm{rad} / \mathrm{s}^2$ ?
b. What is the final angular speed of the claw?
c. What is the tangential acceleration of the tip of the claw?
d. How fast is the tip of the claw moving at the end of its motion?

What is the angular position in radians of the minute hand of a clock at (a) 5:00, (b) 7:15, and (c) 3:35?

Three pairs of balls are connected by very light rods as shown in what we discussed earlier. Rank in order, from smallest to largest, the moments of inertia $I_1, I_2$, and $I_3$ about axes through the centers of the rods.

The 1.00-cm-long second hand on a watch rotates smoothly. a. What is its angular velocity? b. What is the speed of the tip of the hand?

The earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. a. Through what angle do you turn, relative to the earth, if you fly from Kampala to Singapore? Give your answer in both radians and degrees. b. The flight from Kampala to Singapore take 9 hours. What is the plane's angular speed relative to the earth?

The rotating blade of a blender turns with constant angular acceleration $1.50 \mathrm { rad } / \mathrm { s } ^ { 2 }$. (a) How much time does it take to reach an angular velocity of 36.0 rad/s, starting from rest? (b) Through how many revolutions does the blade turn in this time interval?

What is the speed of a point on the earth's surface located at 2/5 of the length of the arc between the equator and the pole, measured from equator? (Hint: what is the radius of the circle in which the point moves?)

The earth’s radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the plane’s angular velocity with respect to the earth’s surface? Give your answer in $^ \circ/h$.

The crankshaft in a race car goes from rest to 3000 rpm in 2.0 s. a. What is the crankshaft's angular acceleration? b. How many revolutions does it make while reaching 3000 rpm?

A double axel is a figure-skating jump in which the skater makes 2.5 revolutions in the air. If a skater is in the air for 0.66 s during a double axel, what is her average angular speed to the nearest degree per second?