Question

A merry-go-round is rotating at the rate of 32 rev/min. Express the rotational velocity in?

1) 32 revolutions per minute
2) 32 radians per minute
3) 32 degrees per minute
4) 32 meters per second

Answer 1

The rotational velocity of 32 revolutions per minute can be expressed as 32 rev/min, 64π radians per minute, and 11,520 degrees per minute. Conversion to meters per second requires additional data.

Step-by-step explanation:

The student asked how to express the rotational velocity of a merry-go-round rotating at a rate of 32 revolutions per minute (rev/min) in various units. Here are the conversions:

• Revolutions per minute: The given is already in 32 rev/min, so no conversion is needed for this unit.
• Radians per minute: Since one revolution is equal to 2π radians, to convert from revolutions to radians, multiply the number of revolutions by 2π. 32 rev/min × 2π rad/rev = 64π rad/min.
• Degrees per minute: One revolution is equal to 360 degrees, so the conversion is 32 rev/min × 360°/rev = 11,520°/min.
• Meters per second: This conversion requires additional information, such as the radius of the merry-go-round, to calculate the linear velocity from the angular velocity. Without the radius, the conversion to meters per second cannot be completed.