Exercise 9.16 Part A Through what total angle did the wheel turn between t 0 and

Question

Exercise 9.16 Part A Through what total angle did the wheel turn between t 0 and the time it stopped? Att 0 a grinding wheel has an angular velocity of 20.0 rad/s. It has a constant angular acceleration of 30.0 rad/s2 until a circuit breaker trips at time t1.80 s. From then on, it turns through an angle 440 rad as it coasts to a stop at constant angular acceleration rad Submit My Answers Give Up Part B At what time did it stop? Submit My Answers Give Up Part C What was its acceleration as it slowed down? rad/s2

Explanation / Answer

at t = 0, wo = 20 rad/s

alfa = 30.0 rad/s^2

at t = 1.8s,

w1 = wo + alfa*t

= 20 + 30.0*1.8

= 74 rad/s

A) Total angular displacement = angular displacament in firce 1.8s + 440 rad

= 20*1.8 + 0.5*30*1.8^2 + 440

= 524.6 rad <<<<<<<<----------------Answer

B) angular acceleration when power is cut, alfa' = (w2^2 - wi^1)/(2*theta')

= (0^2 - 74^2)/(2*440)

= -6.22 rad/s^2

time taken to stop, t' = (w2 - w1)/alfa'

= (0 - 74)/(-6.22)

= 11.9 s

the time where it stops, t = 1.8 + 11.9

= 13.7 s   <<<<<<<<----------------Answer

c) alfa' = -6.22 rad/s^2 <<<<<<<<----------------Answer

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