A solid disc of 4.00m diameter is rotating around its axes throughits center, ha

Question

A solid disc of 4.00m diameter is rotating around its axes throughits center, has an initial angular velocity of 2.60 rev/min. A constant angular acceleration equal to 1.800rad/s2 is acting on the wheel, during thetime, t = 4.20s. (a) What is the angular velocity at the end of4.20 sec? (b) Through what angle in degrees has the wheelturned between t=0 and t=4.2s? (c) What is the linear velocity of the point onthe rim at the end of 4.20 sec? (a) What is the angular velocity at the end of4.20 sec? (b) Through what angle in degrees has the wheelturned between t=0 and t=4.2s? (c) What is the linear velocity of the point onthe rim at the end of 4.20 sec?

Explanation / Answer

initial angular velocity = 2.60 rev/min = 0.272272 rad/s . (a)    final angular velocity = initial ang vel + acc * time =  0.272272 + 1.800 * 4.20 = .          =   7.832 rad/s . (b)   total angle = average speed *time = (1/2) (0.272272 + 7.832) *4.20 = .            =   17.02 radians . (c) linear velocity = angular velocity *radius = 7.832 * 2.00 =    15.66 m/s

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