Question

What is the angular velocity of a 75.0-cm-diameter tire on an automobile traveling at 90.0 km/h?

a) 40.2 rad/s
b) 80.5 rad/s
c) 120.8 rad/s
d) 160.0 rad/s

Answer 1

The angular velocity of the tire is approximately 66.7 rad/s.

Step-by-step explanation:

To calculate the angular velocity of a tire on an automobile, we need to use the formula:

Angular velocity = Linear velocity / Radius

First, we convert the given linear velocity of 90.0 km/h to meters per second (m/s) by dividing by 3.6:

90.0 km/h = 90.0 ÷ 3.6 = 25.0 m/s

Next, we convert the tire's diameter of 75.0 cm to radius by dividing by 2:

Tire radius = 75.0 cm ÷ 2 = 37.5 cm = 0.375 m

Finally, we substitute the values into the formula:

Angular velocity = 25.0 m/s / 0.375 m = 66.7 rad/s

Therefore, the angular velocity of the tire is approximately 66.7 rad/s.