A wheel with a radius of 0.5 meters is rotating at 60 revolutions per minute (rpm). Calculate its angular velocity in radians per second and the tangential velocity of a point on the rim.
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To convert revolutions per minute (rpm) to radians per second, we need to multiply by 2π/60 since there are 2π radians in a complete revolution and 60 seconds in a minute.
Angular velocity = (60 rpm) * (2π radians/1 revolution) * (1 minute/60 seconds) = π radians/second
Therefore, the angular velocity of the wheel is π radians/second.
To find the tangential velocity of a point on the rim of the wheel, we can use the formula:
Tangential velocity = angular velocity * radius
Tangential velocity = π radians/second * 0.5 meters = 0.5π meters/second
Therefore, the tangential velocity of a point on the rim of the wheel is 0.5π meters/second.
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