Question

A technician is testing a computer-controlled, variable-speed motor. She attaches a thin disk to the motor shaft, with the shaft at the center of the disk. The disk starts from rest, and sensors attached to the motor shaft measure the angular acceleration ?z of the shaft as a function of time. The results from one test run are shown in (Figure 1) .

Figure 1 of 1 α. (rad/s~) 4 2 t (s) 0 1.0 2.0 3.0 4.0 5.0 6.0

a) Through how many revolutions has the disk turned in the first 5.0 s?

b)What is the angular velocity, in rad/s, of the disk at t = 5.0 s.

c)What is the angular velocity, in rad/s, of the disk when it has turned through 2.00 rev.

Answer 1

(a)From the graph, the slope is equal to Hence, Slope = α6 The angular acceleration of the disk is, dt Integrate the equation on both sides, The angular displacment of the disk is, At t 5 s, then Δθ =25 rad-25 rad: _lrev (b)The angular velocity of the sak at t = 5 s is, 0--(5 s)' = 15 rad/s (c)The angular displacement disk is, (55) Dr rad 2Trad t l rev5 rev t - 3.975s Hence, the angular velocity of the disk is, ω--(3.975 s). 9.48 rad/s