Question

A car is traveling at a speed of 62mph. The radius of its tires are 17 inches. What is the angular speed of the tires in rad/min? Round to the nearest whole number.

Answer 1

To find the angular velocity of the car tires, we can use the angular velocity formula:

`v=rw`

First, we will need to derive from this equation the equation to find angular velocity as this gives us the speed.

`\begin{gathered} v=rw \\ w=(v)/(r) \end{gathered}`

Now, we need to convert our values from mph to m/s.

1 mph = 0.44704 m/s

62 * 0.44704 = 27.71648 m/s = v

Then, we need to find the radius of the tire in meters.

1 inch = 0.0254 meters

17 * 0.0254 = 0.4318 m = r

Now, we will replace these values with the ones in the equation.

`w=(27.71648)/(0.4318)=64.18823529`

Finally, we can round this to be easier to interpret:

The angular speed of the tire is 64.19 radians/minute, or more compactly: 64.19 rad/min.