Calculate the angular velocity

A pulley driving a belt has a diameter of 300mm and its turning at 2700rpm. Find the angular velocity of the pulley and the linear velocity, assume that there is no slip.
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2700rpm is 2700*300π mm/min=2700*5π mm/s, because I revolution = πd (d=diameter) the circumference of the pulley. 2700 rpm is 2700*360=972000 degrees per min = 16200 degrees/sec; or since 360 degrees = 2π radians, this is 5400 radians per minute or 90 radians per sec. The linear speed is 2700*5π mm/s=13500π mm/s=42411.5mm/s or 42.4115 m/s.

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