A discus thrower starts from rest and begins to rotate with a constant angular acceleration of $2.2 \mathrm{rad} / \mathrm{s}^2$. How many revolutions does it take for the discus thrower's angular speed to reach $6.3 \mathrm{rad} / \mathrm{s}$ ?

After fixing a flat tire on a bicycle you give the wheel a spin. If its initial angular speed was $6.35 \mathrm{rad} / \mathrm{s}$ and it rotated $14.2$ revolutions before coming to rest, what was its average angular acceleration?

How many revolutions does it take for the discus thrower's angular speed to reach 5.7 rad/s?

The angular speed of a propeller on a boat increases with constant acceleration from $12 \mathrm{rad} / \mathrm{s}$ to $26 \mathrm{rad} / \mathrm{s}$ in $2.5$ revolutions. What is the acceleration of the propeller?

A discus thrower (with arm length of $1.2 \mathrm{~m}$ ) starts from rest and begins to rotate counterclockwise with an angular acceleration of $2.5 \mathrm{rad} / \mathrm{s}^2$. a) How long does it take the discus thrower's speed to get to $4.7 \mathrm{rad} / \mathrm{s}$ ? b) How many revolutions does the thrower make to reach the speed of $4.7 \mathrm{rad} / \mathrm{s}$ ? c) What is the linear speed of the discus at $4.7 \mathrm{rad} / \mathrm{s}$ ? d) What is the linear acceleration of the discus thrower at this point? e) What is the magnitude of the centripetal acceleration of the discus thrown? f) What is the magnitude of the discus's total acceleration?

A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for $10.2 \mathrm{~s}$ before coming to rest. If its initial angular speed was $3850 \mathrm{rpm}$, what is the magnitude of its angular deceleration?

A discus thrower accelerates a discus from rest to a speed of 25.0 m/s by whirling it through 1.25 rev. Assume the discus moves on the arc of a circle 1.00 m in radius. (a) Calculate the final angular speed of the discus. (b) Determine the magnitude of the angular acceleration of the discus, assuming it to be constant. (c) Calculate the time interval required for the discus to accelerate from rest to 25.0 m/s.

A ceiling fan is rotating at $0.96 \mathrm{rev} / \mathrm{s}$. When turned off, it slows uniformly to a stop in $2.4 \mathrm{~min}$. How many revolutions does the fan make in this time? Find the number of revolutions the fan must make for its speed to decrease from $0.96 \mathrm{rev} / \mathrm{s}$ to $0.48 \mathrm{rev} / \mathrm{s}$

The Ruby-throated Hummingbird (Archillochus colubris) can flap its wings with an angular speed of $346 \mathrm{rad} / \mathrm{s}$. What is the period of its flapping motion?

A spot of paint on a bicycle tire moves in a circular path of radius 0.33 m. When the spot has traveled a linear distance of 1.95 m, through what angle has the tire rotated? Give your answer in radians.

A 0.50-kg croquet ball is initially at rest on the grass. When the ball is struck with a croquet mallet, the average force exerted on the ball is 230 N. If the ball's speed after being struck is 3.2 m/s, how long was the mallet in contact with the ball?

As you drive down the highway, the top of your tires are moving with a speed $v$. What is the reading on your speedometer?

After fixing a flat tire on a bicycle you give the wheel a spin. For what length of time did the wheel rotate?

A ceiling fan is rotating at $0.96 \mathrm{rev} / \mathrm{s}$. When turned off, it slows uniformly to a stop in $2.4 \mathrm{~min}$. How many revolutions does the fan make in this time?