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

w'=(1/2)w

Step-by-step explanation:

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

`\omega=(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'=(v)/(r')=(v)/(2r)=(1)/(2)(v)/(r)=(1)/(2)\omega\\\\\omega'=(1)/(2)\omega`

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