Question

A wheel of radius 30.0 cm is rotating at a rate of 2.20 revolutions every 0.0910 s. What is the linear speed of a point on the wheels rim?

Answer 1

Step-by-step explanation:

First, we need to calculate the frequency of the wheel, so if it is rotating at a rate of 2.20 revolutions every 0.0910 seconds, the frequency is:

`f=\frac{2.20\text{ revolutions}}{0.0910\text{ seconds}}=24.16\text{ Hz}`

Then, the magnitude of the angular velocity is equal to:

`w=2\pi f=2(3.14)(24.16)=151.9\text{ rad/s}`

Finally, we can calculate the linear speed as the angular velocity times the radius, so:

`v=w\cdot r=(151.9\text{ rad/s)(30 cm) = 4557.04 m/s}`

Therefore, the linear speed is 45.47 m/s