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A bicycle with 24-inch diameter wheels is traveling at 12 mi/h.

What is the exact angular speed of the wheels in rad/min?
Number rad/min:

How many revolutions per minute do the wheels make?
The answer must be rounded to three decimal places by the way.

User Jenina
by
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1 Answer

6 votes

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Answer:

  • 1056.000 radians per minute
  • 168.068 revolutions per minute

Explanation:

The linear speed 12 mi/h translates to inches per minute as follows:

(12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min

The relationship between arc length and angle is ...

s = rθ

For a constant radius, the relationship between linear speed and angular speed is ...

s' = rθ'

θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min

There are 2π radians in one revolution, so this is ...

(1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min

User Rocksteady
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