A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity assuming a constant speed?

A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?

A man stands on a merry-go-round that is rotating at 2.5 rad/s. If the coefficient of static friction between the man's shoes and the merry-go-round is

$$μ_S = 0.5,$$

how far from the axis of rotation can he stand without sliding?

A wheel 1.0 m in diameter rotates with an angular acceleration of 4.0 rad/s². (a) If the wheel's initial angular velocity is 2.0 rad/s, what is its angular velocity after 10 s? (b) Through what angle does it rotate in the 10-s interval? (c) What are the tangential speed and acceleration of a point on the rim of the wheel at the end of the 10-s interval?

Using the parallel axis theorem, what is the moment of inertia of the rod of mass $m$ about the axis shown below?

On takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular velocity from rest at a rate of ω = (25.0t)rad/s for 3.0 s. (a) What is the instantaneous angular velocity of the propellers at t = 2.0 s? (b) What is the angular acceleration?

A rotating wheel has a constant angular acceleration. It has an angular velocity of 5.0 rad/s at time t=0 s, and 3.0 s later has an angular velocity of 9.0 rad/s. What is the angular displacement of the wheel during the 3.0-s interval? (a) 15 rad (b) 21 rad (c) 27 rad (d) There is not enough information given to determine the angular displacement.

$$\begin{array}{l} \text{ Find the derivative of the function. } \end{array}$$

$$s ( t ) = \left( 3 t ^ { 2 } - 2 t + 5 \right) ^ { - 2 }$$

A satellite in the shape of a sphere of mass 20,000 kg and radius 5.0 m is spinning about an axis through its center of mass. It has a rotation rate of 8.0 rev/s. Two antennas deploy in the plane of rotation extending from the center of mass of the satellite. Each antenna can be approximated as a rod has mass 200.0 kg and length 7.0 m. What is the new rotation rate of the satellite?

On takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular velocity from rest at a rate of $\omega=(25.0 \mathrm{t}) \mathrm{rad} / \mathrm{s}$ for $3.0 \mathrm{~s}$. (a) What is the instantaneous angular velocity of the propellers at $t=2.0 \mathrm{~s}$ ? (b) What is the angular acceleration?

A 90-kg mountain climber hangs from a nylon rope and stretches it by 25.0 cm. If the rope was originally 30.0 m long and its diameter is 1.0 cm, what is Young's modulus for the nylon?

A vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular acceleration of 5.0 rad/s² around a fixed axis through its center counterclockwise. (a) Where is the point that is initially at the bottom of the wheel at t = 10 s? (b) What is the point's linear acceleration at this instant?

Calculate the angular velocity of Earth.

When the spring on a toy gun is compressed by a distance x, it will shoot a rubber ball straight up to a height of h. Ignoring air resistance, how high will the gun shoot the same rubber ball if the spring is compressed by an amount 2x? Assume

$$x \ll h$$

.