10.2 Rotation with Constant Angular Acceleration

A centrifuge used in DNA extraction spins at a maximum rate of 7000 rpm, producing a “g-force” on the sample that is 6000 times the force of gravity. If the centrifuge takes 10 seconds to come to rest from the maximum spin rate: (a) What is the angular acceleration of the centrifuge? (b) What is the angular displacement of the centrifuge during this time?

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

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

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 wheel 1.0 m in radius rotates with an angular acceleration of $4.0 \text{rad} / \text{s}^{2}$. (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 circular disk of radius 10 cm has a constant angular acceleration of $1.0 \text{rad} / \text{s}^{2}$; 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 $t = 5.0 \text{s} ?$

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?