At time t=0 a grinding wheel has an angular velocity of 25.0 rad/s . It has a co

Question

At time t=0 a grinding wheel has an angular velocity of 25.0 rad/s . It has a constant angular acceleration of 32.0 rad/s2 until a circuit breaker trips at time t = 2.30 s . From then on, the wheel turns through an angle of 435 rad as it coasts to a stop at constant angular deceleration.

A)Through what total angle did the wheel turn between t=0 and the time it stopped? Express your answer in radians.

B) Through what total angle did the wheel turn between t=0 and the time it stopped?Express your answer in seconds.

C) What was the wheel's angular acceleration as it slowed down? Express your answer in radians per second per second.

Explanation / Answer

v = v° + 1/2 a t^2
v° = 25 rad /s
a = 32 rad /s2
t = 2.3s
e = v°t + 1/2 a t^2 = 25 *2 + 0.5 * 32 * (2.3)^2 = 134.64 rad
v = v° + a t = 25 + 32 *2.3= 98.6 rad /s

total angle did the wheel turn between t=0 and the time it stopped 134.64 + 435 = 569.64 rad

t =435 / vmoy = 434 /(0.5*98.6) = 8.8 s +2 = 10.8s

wheel's angular acceleration as it slowed down

a = d v / d t = 98.6 / 8.8 = - 11.2 rad /s2

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