At time t =0 a grinding wheel has an angular velocity of 22.0 rad/s . It has a c

Question

At time t=0 a grinding wheel has an angular velocity of 22.0 rad/s . It has a constant angular acceleration of 33.0 rad/s2 until a circuit breaker trips at time t = 2.50 s . From then on, the wheel turns through an angle of 437 rad as it coasts to a stop at constant angular deceleration.

Part A

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

Express your answer in radians.

Part B

At what time does the wheel stop?

Express your answer in seconds.

Part C

What was the wheel's angular acceleration as it slowed down?

Express your answer in radians per second per second.

Explanation / Answer

given,

angular velocity = 22.0 rad/s

acceleration = 33.0 rad/s2

time t = 2.50 s

from first equation of motion

v = u + at

v = 22 + 33 * 2.5

final veocity = 104.5 rad/sec

total angle covered till this time

s = ut + 0.5 * a * t^2

s = 22 * 2.5 + 0.5 * 33 * 2.5^2

s = 158.125 rad

total angle did the wheel turn between t=0 and the time it stopped = 158.125 + 437

total angle did the wheel turn between t=0 and the time it stopped = 595.125 rad

after current is turned off

v^2 = u^2 + 2 * a * s

0^2 = 104.5^2 + 2 * a * 437

wheel's angular acceleration as it slowed down a = -12.4945 rad/sec^2

v = u + at

0 = 104.5 - 12.4945 * t

t = 8.3637 sec

time after which the wheel stop = 8.3637

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