6.2.2 Rotation with Constant Angular Acceleration

Question 1

Rotation with Constant Angular Acceleration

Answer 1

• The motion of an object in one dimension under constant acceleration can be completely described by a set of equations. An analogous set of equations can be used to describe rotational motion with constant angular acceleration.
• The equations describing rotational motion with constant angular acceleration:

Question 2

A wheel turns through an angle of 300 rad in 10.0 s. The wheel’s angular speed at the end of the period is 40 rad / s. If the angular acceleration is constant, which of the following represents the angular speed of the wheel at the beginning of the 10.0 s interval?

Answer 2

w0 = 2 delta theta /t - w

Question 3

A computer hard drive rotates at 7,500 rpm. If it begins decelerating at 100 rad / s2, how long does it take to rotate through 15,000 revolutions?

Answer 3

250 pi +- sqrt[(250pi)^2 - 2(100)(30,000pi)] / 100

Question 4

A grindstone is spinning with a constant angular velocity of 500 rad/s when a break is applied, creating an angular acceleration -a (rev/s^2). Which of the following expressions represents the number of turns the grindstone makes after the brake is applied?

Answer 4

w0^2/8pi^2a

Question 5

A car tire originally rotating at 500 rad / s undergoes a constant angular deceleration of 5.00 rad / s2. Which of the following represents the tire’s angular speed after it has turned through an angle of 628 rad?

Answer 5

sqrt(w0^2 + 2a delta theta)

Question 6

A car engine starts from rest, and 2s later, it is rotating with an angular speed of 1,000 rev/min. Which of the following is the expression for acceleration in rad/s^2?

Answer 6

2piw/60t

Question 7

A grindstone is spinning with a constant angular velocity of 500 rad / s when a brake is applied, slowing the grindstone to a halt in 20 s. Which of the following expressions represents the angular acceleration of the grindstone after the brake is applied?

Answer 7

-500/20

Question 8

A car tire is rotating with an initial angular velocity of 6,000 rev / min when the driver presses the brake pedal. In 400 rev, the angular velocity is reduced to 600 rev / min. If the angular acceleration is constant, which of the following expressions gives the appropriate result for the duration of this acceleration?

Answer 8

2 delta theta / w + w0

Question 9

A carpenter’s drill accelerates to 2,000 rpm in 2.80 s. Which of the following represents its angular acceleration?

Answer 9

23.8 pi rad/s^2