At time t=0 a grinding wheel has an angular velocity of 26.0 rad/s. It has a constant angular acceleration of 25.0 rad/s^2 until a circuit breaker trips at time t = 2.50 s. From then on, the wheel turns through an angle of 440 rad as it coasts to a stop at constant angular deceleration.

Through what total angle did the wheel turn between t=0 and the time it stopped? At what time does the wheel stop? What was the wheel's angular acceleration as it slowed down?

The equations of motions will be applied in this question; except that in this case it will be angular motion instead of linear motion.

We use the formula

v = u + at; to determine the final velocity of before the circuit breaker trips.

v = 26 + 2.5 x 25

= 88.5 rad/s

Total angle covered before circuit breaker trips:

2as = v² - u²

s = (88.5² - 26²) / 2 (25)

s = 143.125 rad

Angle covered before stopping after trip = 440 rad

Total angle covered from start to finish:

143.125 + 440

= 583.125 rad

Acceleration as wheel stops:

2as = v² - u²; v = 0

a = - (88.5²) / 2 (440)

a = 0.1 rad/s²

Time to stop:

v = u + at

0 = 88.5 - 0.1t

t = 885 seconds

Total time: 2.5 + 885

= 887.5 seconds