Answer to Question #253019 in Mechanics | Relativity for John

Question

lt is desired that the outer edge of a grinding wheel 9.0 cm in radius
moves at a rate of 6.Om/s. (a) Determine the angular speed of the
wheel. (b) What length of thread could be wound on the rim of the
wheel in 3.0 s when it is turning at this rate

Answer 1

A.

Angular speed $ω = \frac{Translational \; speed \; v}{ radius \; r}$

thus $ω = \frac{v}{r} = \frac{6 ms⁻¹}{0.09 m} = 66.67 \;rad/s$

B.

As we know, length of thread that can be wound on spinning wheel in 3 s = $translational \; speed × time = 6×3=18 m$