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Need help with angular velocity?
How to get answer in radian per hour?
A motorcyle wheel has a diameter of 14 in. If the vehicle going 55 miles per hour, what is the angular velocity, in radians per hour, of a point on the edge of wheel?
So far, I did 14/2 to get radius which is 7 in.
1 Answer
- JonathanLv 79 years agoFavorite Answer
Since the vehicle is travelling at 55 mph, that's also the speed of the wheel. That's also the same as 968 inches/second. Since you know that the circumference of the motorcycle wheel is πD or π⋅14", you can just do this computation:
1. (968 in ⁄ sec) ⁄ (π⋅14 in) ≈ 22.008855 Hertz
The wheel must be rotating about 22 revolutions a second. Which is lots of radians per second. And lots more when you multiply by 3600 to get how many per hour.
Your final calculation will be:
2. 22.008855 Hertz ⨯ 2π ⨯ 3600 sec ⁄ hr ≈ 497829 radians ⁄ hr
That reads as "22 revolutions per second times 2π radians per revolution times 3600 seconds per hour gives 497829 radians per hour." (Note that the units of seconds cancel out and the units of revolutions cancel out, leaving only radians per hour. As it should be.)
