Question

You are traveling forward in a car at 20 m/s. Your car tires have a radius of 33 cm.

What is the angular velocity of each tire in rad/s?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the angular velocity of each tire, we need to convert the linear velocity of the car into angular velocity.

The linear velocity of the car can be defined as the product of the angular velocity (ω) and the radius of the tire (r). Therefore, we have the formula:

v = ω * r

where v is the linear velocity, ω is the angular velocity, and r is the radius of the tire.

In this case, the linear velocity (v) is given as 20 m/s and the radius (r) of the tire is given as 33 cm.

First, we convert the radius from centimeters to meters:
33 cm = 33/100 m = 0.33 m

Now, we can rearrange the formula to solve for ω:
ω = v / r

Plugging in the values for v and r, we get:
ω = 20 m/s / 0.33 m
ω ≈ 60.61 rad/s

Therefore, the angular velocity of each tire is approximately 60.61 rad/s.