a shaft is turning at angular speed w at time t=0. Thereafter, it\'s angular acc

Question

a shaft is turning at angular speed w at time t=0. Thereafter, it's angular acceleration is given by (angular acceleration) = A+Bt.
(a) find the angular speed of the shaft at time t.
(w(t) = ?)
(b) through what angle does it turn between t=0 and t?
(Angular displacement = ?) a shaft is turning at angular speed w at time t=0. Thereafter, it's angular acceleration is given by (angular acceleration) = A+Bt.
(a) find the angular speed of the shaft at time t.
(w(t) = ?)
(b) through what angle does it turn between t=0 and t?
(Angular displacement = ?) a shaft is turning at angular speed w at time t=0. Thereafter, it's angular acceleration is given by (angular acceleration) = A+Bt.
(a) find the angular speed of the shaft at time t.
(w(t) = ?)
(b) through what angle does it turn between t=0 and t?
(Angular displacement = ?)

Explanation / Answer

a) w(t) = integral A+Bt = At + Bt^2/2 + C

at t=0 ,  w(t) =  w , => C =  w

=> w(t) = At + Bt^2/2 + w

b) Angular displacement = integral w(t)dt = At^2/2 + Bt^3/6 + wt + D

at t=0 angular displacement = 0 => D=0

=> Angular displacement = At^2/2 + Bt^3/6 + wt

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