Question

Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is one-half (1/2) the radius of wheel 1. The angular velocity of wheel 2 is:

Answer 1

Answer:

w'=(1/2)w

Explanation:

In order to calculate the angular velocity of the second wheel, you use the following formula:

$\omega=\frac{v}{r}$      (1)

v: speed of the wheel 1 = speed of the wheel 2

r: radius of the wheel 1

For the second wheel you have:

r'=2r

You replace this value of r' in the following equation:

$\omega'=\frac{v}{r'}=\frac{v}{2r}=\frac{1}{2}\frac{v}{r}=\frac{1}{2}\omega\\\\\omega'=\frac{1}{2}\omega$

The angular velocity of the second wheel is one half of the angular velocity of the first wheel