A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of 12.0 rad/s in 3.00 s. Find (a) the magnitude of the angular acceleration of the wheel and (b) the angle in radians through which it rotates in this time interval.

Find the net torque on the wheel in the given figure about the axle through O if a=10.0 cm and b=25.0 cm.

How does this rotation affect the shape of Earth?

A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 $^ { \circ }$ with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.

A rotating wheel with diameter 0.600 m is speeding up with constant angular acceleration. The speed of a point on the rim of the wheel increases from 3.00 m/s to 6.00 m/s while the wheel turns through 4.00 revolutions. What is the angular acceleration of the wheel?

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 rotating wheel accelerates at a constant rate from an angular speed of 24 rad/s to 36 rad/s in a time interval of 3 s. What is the angle in radians through which the wheel rotates?

A wheel released from rest is rotating with constant angular acceleration of $2.6 \mathrm{rad} / \mathrm{s}^2$. At $6.0 \mathrm{~s}$ after the release:

$(c)$ How many revolutions has it completed?

A disk starts from rest and rotates with constant angular acceleration. If the angular velocity is $\omega$ at the end of the first two revolutions, then at the end of the first eight revolutions it will be
A. $\sqrt{2} \omega$.
B. $2 \omega$.
C. $40$
D. $16\omega$

What is the angular acceleration of the wheel?

A bar on a hinge starts from rest and rotates with an angular acceleration $\alpha=10+6 t,$ where $\alpha$ is in $\mathrm{rad} / \mathrm{s}^{2}$ and t is in seconds. Determine the angle in radians through which the bar turns in the first 4.00 s.

A wheel released from rest is rotating with constant angular acceleration of $2.6 \mathrm{rad} / \mathrm{s}^2$. At $6.0 \mathrm{~s}$ after the release:

$(b)$ Through what angle has the wheel turned?

Solve each equation or inequality. $|6-3 x|<-11$

(a) As we discussed earlier three points in the operation of the ballistic pendulum were discussed. The projectile approaches the pendulum we discussed earlier the situation just after the projectile is captured in the pendulum. as we discussed earlier, the pendulum arm has swung upward and come to rest at a height $h$ above its initial position. Prove that the ratio of the kinetic energy of the projectile-pendulum system immediately after the collision to the kinetic energy immediately before is $m_1 /\left(m_1+m_2\right)$.
(b) What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before?
c) A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth?