Question

A 10 cm diameter disc of mass 100g was spinning at 4000 revolutions / minute . it was brought to a stop in 10 seconds. what was the angular acceleration , tangential acceleration and the total angle covered in radians? what is the torque?

Answer 1

here,

diameter , d = 10 cm = 0.1 m

radius ,r = d/2 = 0.05 m

mass , m = 0.1 kg

initial angular speed , w0 = 4000 rev/min = 418.7 rad/s

time taken , t = 10 s

let the angular accelration be alpha

0 = w0 + alpha * t

0 = 418.7 + alpha * 10

alpha = - 41.87 rad/s^2

the tangential accelration , a = alpha * r = - 2.1 m/s^2

the angle covered , theta = w0 * t + 0.5 * alpha * t^2

theta = 418.7 * 10 - 0.5 * 41.87 * 10^2 rad

theta = 2093.5 rad

torque , T = I * alpha

T = 0.5 * m * r^2 * alpha

T = 0.5 * 0.1 * 0.05^2 * (-41.87)

T = - 5.2 * 10^-3 N.m