Question

You are driving down the highway at 65 m p h, which is 29 m/s. Your tires have a radius of 0.30 m. a. How many times per second does each tire rotate? b. What is the speed of a point at the top of a tire, relative to the ground?

Answer 1

To solve this problem we will apply the concepts related to linear velocity and angular velocity to perform the respective conversion with the given values. To find the velocity in the upper part of the tire we will use the mathematical relation that expresses that it is twice the linear velocity. Let's start

PART A)

`\omega = (v)/(r)`

`\omega = (29)/(0.3)`

`\omega = 96.66 rad/s`

Now we now that
`2\pi rad = 1 rev`, then

`\omega = 96.66rad/s ((1 rev)/(2\pi rad))`

`\omega = 15.38rev/s`

PART B)

`v = 2v_0`

`v = 2(29)`

`v = 58m/s`