Question

At t=0 a grinding wheel has an angular velocity of 21.0 rad/s . It has a constant angular acceleration of 33.0 rad/s2 until a circuit breaker trips at time t = 1.70 s . From then on, it turns through an angle 440 rad as it coasts to a stop at constant angular acceleration.

1.Through what total angle did the wheel turn between t=0 and the time it stopped?

2.At what time did it stop?

3.What was its acceleration as it slowed down?

Answer 1

here,

initial angular velocity , w0 = 21 rad/s

t1 = 1.7 s

the angular accelration , alpha1 = 33 rad/s

the angular speed at t1 , w1 = w0 + alpha1 * t1

w1 = 21 + 33 * 1.7 = 77.1 rad/s

a)

the total angle covered , theta = 440 + (w0 * t1 + 0.5 * alpha1 * t1^2)

theta = 400 * ( 21 * 1.7 + 0.5 * 33 * 1.7^2)

theta = 483.4 rad

b)

let the time taken to stop and angular accelration be t2 and alpha2

w^2 - w0^2 =2 * alpha2 * theta0

0 - 77.1^2 = 2 * alpha2 * 400

alpha2 = - 7.43 rad/s^2

and

0 = w1 + alpha2 * t2

0 = 77.1 - 7.43 * t2

t2 = 10.4 s

the time taken to stop is 10.4 s

c)

the accelration to slow down is - 7.43 rad/s^2