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?

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?

At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of $30.0 \text { rad} / \mathrm { s } ^ { 2 }$ until a circuit breaker trips at t = 2.00 s. From then on, it turns through 432 rad as it coasts to a stop at constant angular acceleration. Through what total angle did the wheel turn between t = 0 and the time it stopped?

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 wind turbine is rotating counterclockwise at 0.5 rev/s and slows to a stop in 10 s. Its blades are 20 m in length. (a) What is the angular acceleration of the turbine? (b) What is the centripetal acceleration of the tip of the blades at t = 0 s? (c) What is the magnitude and direction of the total linear acceleration of the tip of the blades at t = 0 s?

A Ferris wheel rotates at an angular velocity of 0.24 rad/ s. Starting from rest, it reaches its opera ting speed with an average angular acceleration of

$$0.030 \mathrm { rad } / \mathrm { s } ^ { 2 }.$$

How long does it take the wheel to come up to operating speed?

The angular velocity of a rotating rigid body increases from 500 to 1500 rev/min in 120 s. (a) What is the angular acceleration of the body? (b) Through what angle does it turn in this 120 s?

Graph each inequality. 2(3-5)<k

What are the advantages of phytoremediation over acid leaching in treating contaminated soils?

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.

Solve the system by using a graph or table.

$$\left\{ \begin{array} { l } { y = - 2 ( x - 3 ) ^ { 2 } + 9 } \\ { y = - 4 x + 3 } \end{array} \right.$$

A 6090 kg space probe moving nose-first toward Jupiter at 105 m/s relative to the Sun fires its rocket engine, ejecting 80.0 kg of exhaust at a speed of 253 m/s relative to the space probe. What is the final velocity of the probe?

In a certain series RLC circuit being driven at a frequency of 60.0 Hz, the maximum voltage across the inductor is 2.00 times the maximum voltage across the resistor and 2.00 times the maximum voltage across the capacitor. By what angle does the current lag the generator emf?

A series RLC circuit is driven in such a way that the maximum voltage across the inductor is 1.50 times the maximum voltage across the capacitor and 2.00 times the maximum voltage across the resistor. What is $\pi$ for the circuit?