A cyberpunk bloke is on one of those insane big wheeled bikes. The radius of the

Question

A cyberpunk bloke is on one of those insane big wheeled bikes. The radius of the wheel is 1.5 meters a) If the wheel has a displacement of 45 degrees in one second, what is the angular velocity of the big wheel in rad/s? b) What would be the corresponding tangential/linear velocity of the big wheel? C) If the wheel goes from 1 rad/sec to 5 rad/sec in the course of 10 seconds, what is the angular acceleration of the big wheel? d) If the bike is now traveling at 10 mph (4.5 m/s) what is the angular velocity of the big wheel?

Explanation / Answer

a) Pi radians = 180 degrees

hence 45 degrees = pi/4 radians

therefore, angular velocity = w = pi/4 radians per second or 0.7854 rad/sec

b) Tangential velocity = v = w*R

as R = 1.5 mts

v = 0.7854*1.5 = 1.1781 m/sec

c) angular acceleration = (w2-w1)/time   ( w = angular velocity)

angular acceleration = (5-1)/10 = 0.4 rad/sec2

d) as v = w*R

and v =4.5 and R=1.5

angular velocity = 4.5/1.5 = 3 rad/sec

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