At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 30.0 rad/s2 until a circuit breaker trips at t = 2.00 s. From then on, it turns through 432 rad as it coasts to a stop at constant angular acceleration. (a) Through what total angle did the wheel turn between t = 0 and the time it stopped? (b) At what time did it stop? (c) What was its acceleration as it slowed down?
Solution 16E Step 1: Angular velocity = 24.0 rad/s i 2 Angular acceleration = 30.0 rad /s Time t = 2.0 s Angle = 432 rad Consider = t + 1/2 at 2 f i Substitute values we get 2 2 f 24.0 rad /s × 2s + 1/2 × 30.0 rad /s × 2.0 s e = 108 rad Also consider f + it f 24.0 rad /s + 30.0 rad /s × 2.0 s = 84 rad/s f Step 2 : The total angle did the wheel turn between t = 0 and the time it stopped is = 108 rad + 432 rad f f 539 rad The total angle is 539 rad