A wheel has a constant angular acceleration of 5.0 rad/s². Starting from rest, it turns through 300 rad. (a) What is its final angular velocity? (b) How much time elapses while it turns through the 300 radians?

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 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.

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 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?

A wheel, starting from rest, rotates with a constant angular acceleration of $2.00 \text{~rad/s}^2$. During a certain $3.00 \text{~s}$ interval, it turns through $90.0\text{~ rad}$. What is the angular velocity of the wheel at the start of the $3.00 \text{~s}$ interval?

Analgesics a. relieve allergy symptoms. b. kill harmful bacteria. c. relieve pain. d. soothe itchy skin.

A flywheel has a constant angular deceleration of

$$2.0 rad/s^2.$$

(a) Find the angle through which the flywheel turns as it comes to rest from an angular speed of 220 rad/s. (b) Find the time required for the flywheel to come to rest.

At $t = 0$, a flywheel has an angular velocity of $4.7\text{~ rad/s}$, a constant angular acceleration of $-0.25\text{~ rad/s}^2$, and a reference line at $\theta_0 = 0$. Through what maximum angle

$$θ_max$$

will the reference line turn in the positive direction?

How might continued insurgent attacks in Iraq affect U.S. involvement in the region?

Starting from rest at t = 0, a wheel undergoes a constant angular acceleration. When t = 2.0 s, the angular velocity of the wheel is 5.0 rad/s. The acceleration continues until t = 20 s, when it abruptly ceases. Through what angle does the wheel rotate in the interval t = 0 to t = 40 s?

A thin rod of length 0.75 meters and mass 0.42 kilogram is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed $4.0 \text{~rad/s}$. Neglecting friction and air resistance, find the rod’s kinetic energy at its lowest position.

A wheel turns with a constant angular acceleration of $0.640 \mathrm{rad} / \mathrm{s}^2$.
(a) How much time does it take to reach an angular velocity of $8.00 \mathrm{rad} / \mathrm{s}$, starting from rest?
(b) Through how many revolutions does the wheel turn in this interval?

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?