10.2 Rotation with constant angular acceleration  (Page 4/5)

If a rigid body has a constant angular acceleration, what is the functional form of the angular velocity in terms of the time variable?

If a rigid body has a constant angular acceleration, what is the functional form of the angular position?

If the angular acceleration of a rigid body is zero, what is the functional form of the angular velocity?

A massless tether with a masses tied to both ends rotates about a fixed axis through the center. Can the total acceleration of the tether/mass combination be zero if the angular velocity is constant?

A wheel has a constant angular acceleration of $5.0\text{rad}\text{/}{\text{s}}^2$ . 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?

During a 6.0-s time interval, a flywheel with a constant angular acceleration turns through 500 radians that acquire an angular velocity of 100 rad/s. (a) What is the angular velocity at the beginning of the 6.0 s? (b) What is the angular acceleration of the flywheel?

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?

A flywheel slows from 600 to 400 rev/min while rotating through 40 revolutions. (a) What is the angular acceleration of the flywheel? (b) How much time elapses during the 40 revolutions?

A wheel 1.0 m in diameter rotates with an angular acceleration of $4.0\text{rad}\text{/}{\text{s}}^2$ . (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 vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular acceleration of $5.0\text{rad}\text{/}{\text{s}}^2$ around a fixed axis through its center counterclockwise. (a) Where is the point that is initially at the bottom of the wheel at $t=10\text{s?}$ (b) What is the point’s linear acceleration at this instant?

A circular disk of radius 10 cm has a constant angular acceleration of $1.0\text{rad}\text{/}{\text{s}}^2$ ; at $t=0$ its angular velocity is 2.0 rad/s. (a) Determine the disk’s angular velocity at $t=5.0\text{s}$ . (b) What is the angle it has rotated through during this time? (c) What is the tangential acceleration of a point on the disk at $t=5.0\text{s}?$

The angular velocity vs. time for a fan on a hovercraft is shown below. (a) What is the angle through which the fan blades rotate in the first 8 seconds? (b) Verify your result using the kinematic equations.

A rod of length 20 cm has two beads attached to its ends. The rod with beads starts rotating from rest. If the beads are to have a tangential speed of 20 m/s in 7 s, what is the angular acceleration of the rod to achieve this?