Question

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

Answer 1

Answer:

Angular velocity of tire $\approx 66.67\ s^{-1}$

Explanation:

Given:

Diameter of tire of an automobile =75.0 cm

Linear velocity of automobile = 90.0 km/hr

To find angular velocity of tire.

Diameter of tire in meters = $75\ cm \times \frac{1\ m}{100\ cm}= 0.75\ m$

Radius of tire = $\frac{1}{2}\times diameter=\frac{1}{2}\times 0.75\ m = 0.375\ m$

Linear velocity in meters per second = $\frac{90\ km}{1\ hr}\times \frac{1000\ m}{1\ km}\times \frac{1\ hr}{3600\ s}= 25\ m/s$

Angular velocity $\omega$ is given by :

$\omega=\frac{v}{r}$

where $v$ represents linear velocity and $r$ represents radius of tire.

Plugging in values.

$\omega=\frac{25\ m/s}{0.375\ m}$

∴ $\omega=66.666 s^{-1}\approx 66.67\ s^{-1}$ (Answer)