Question 17 trigonometry

Question

A wheel of radius 6 inches is rotating at 1.75 rad/s. Round answers to 2 decimal places, where necessary. What is the linear speed v?(inch/s), what is the angular speed in RPM? What is the angular speed in degrees/s?

Answer 1

Hi Joelle N.,

We are given the radius in inches, r = 6, and the angular speed in radians per second, ω = 1.75.

Linear speed is equal to angular speed times the radius of rotation, v = ω*r.

v = 1.75*6 = 10.50 inch/s

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For revolutions/minute, RPM, where one revolution equals 2π is:

1.75 rad/s*(60s/1 min)*(1 rev/2π rad) = 1.75*(60)/(2π) rev/min = 16.71 rev/min or 16.71 RPM

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And for angular speed in degrees/s with 180 degrees = π rad:

1.75 rad/s*(180 degrees/π rad) = 100.27 degrees/s

I hope this helps, Joe.