A diver makes 2.5 revolutions on the way from a 10-m-high platform to the water. Assuming zero initial vertical velocity, find the average angular velocity during the dive.

The angular position of a point on a rotating wheel is given by $\theta = 2.0 + 4.0t^2 + 2.0t^3$, where $\theta$ is in radians and t is in seconds. At $t = 0$, what is the point’s angular position?

At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

A good baseball pitcher can throw a baseball toward home plate at 85 mi/h with a spin of 1800 rev/min. How many revolutions does the baseball make on its way to home plate? For simplicity, assume that the 60 ft path is a straight line.

The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What are the angular velocities at $t = 2.0 \text{~s}$.

The masses and coordinates of four particles are as follows: $50\text{~ g}, x = 2.0 \text{~ cm}, y = 2.0\text{~ cm}; 25 \text{~ g}, x = 0, y = 4.0\text{~ cm}; 25\text{~ g}, x = -3.0 \text{~ cm}, y = -3.0\text{~ cm}; 30 \text{~ g}, x = -2.0\text{~ cm}, y = 4.0 \text{~ cm}$. Suppose that we symbolize the answers to (a) and (b) as A and B, respectively. Then what is the answer to (c) in terms of A and B?

A graph of the angular velocity versus time for the rotating disk. For a point on the disk rim, rank the instants a, b, c, and d according to the magnitude of the

radial acceleration, greatest first.

The given figure shows a graph of the angular velocity versus time for the rotating disk of as shown in figure. For a point on the disk rim, rank the instants a, b, c, and d according to the magnitude of the tangential.

The masses and coordinates of four particles are as follows: $50\text{~ g}, x = 2.0 \text{~ cm}, y = 2.0\text{~ cm}; 25 \text{~ g}, x = 0, y = 4.0\text{~ cm}; 25\text{~ g}, x = -3.0 \text{~ cm}, y = -3.0\text{~ cm}; 30 \text{~ g}, x = -2.0\text{~ cm}, y = 4.0 \text{~ cm}$. What is the rotational inertia of this collection about the $z$ axis?

Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s$^2$ , what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?

The masses and coordinates of four particles are as follows: $50\text{~ g}, x = 2.0 \text{~ cm}, y = 2.0\text{~ cm}; 25 \text{~ g}, x = 0, y = 4.0\text{~ cm}; 25\text{~ g}, x = -3.0 \text{~ cm}, y = -3.0\text{~ cm}; 30 \text{~ g}, x = -2.0\text{~ cm}, y = 4.0 \text{~ cm}$. What is the rotational inertia of this collection about the $x$ axis?

The masses and coordinates of four particles are as follows: $50\text{~ g}, x = 2.0 \text{~ cm}, y = 2.0\text{~ cm}; 25 \text{~ g}, x = 0, y = 4.0\text{~ cm}; 25\text{~ g}, x = -3.0 \text{~ cm}, y = -3.0\text{~ cm}; 30 \text{~ g}, x = -2.0\text{~ cm}, y = 4.0 \text{~ cm}$. What is the rotational inertia of this collection about the $y$ axis?

The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (b) At what speed must the train go around a curve with a 1.00 km radius to be at the acceleration limit?

An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. (a) What is the astronaut’s speed if the centripetal acceleration has a magnitude of 7.0 g? (b) How many revolutions per minute are required to produce this acceleration? (c) What is the period of the motion?