A wheel of diameter 70 mm is rotating at 240 rpm Determine t

A wheel of diameter 70 mm is rotating at 240 rpm. Determine the average angular velocity and the corresponding linear velocity of a point on its rim. For the sinusoidal voltage waveform given by v = 40 sin (50 pi t + 0.29) mv, find the amplitude, periodic time, frequency and phase angle in radians and degrees stating whether it is leading or lagging 40 sin 50 pi t.

Solution

angular speed=240 revolutions per minute we just need to transform the unit to radians per minute
we do this by multiplying 240rev/min by 2pi rad/1 rev
therefore, angular speed=480pi rad/min=1508.57rad/min
Linear velocity is given by v=rw=(35)(480pi)=16800pi mm/min=52800 mm/min