Question

A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 700 rad/s2 for 12s, then coasts at a steady angular velocity for another 12s.

What is the speed of the dot at t = 1.0 s?

Through how many revolutions has it turned?

Answer 1

here,

diameter , d = 8 cm

radius , r = d/2 = 4 cm = 0.04 m

angular accelration , alpha = 700 rad/s^2

time taken , t1 = 12 s

t2 = 12 s

at t3 = 1 s

the angular speed of dot , w3 = 0 + alpha * 1 = 700 rad/s

the tangential speed , v3 = r * w3 = 28 m/s

after t1 = 12 , the final angular speed , w1 = 0 + alpha * t1

w1 = 700 * 12 = 8400 rad/s

the total angle , theta = (0 + 0.5 * alpha * t1^2) + w1 * t2

theta = ( 0.5 * 700 * 12^2) + 8400 * 12 rad

theta = 1.51 * 10^5 rad

the number of revolutions , N = theta/2pi

N = 2.41 * 10^4 revolutions