Question

A bicycle has tires of radius 0.35 meters. If the bicycle is traveling at a constant speed of 7.8 m/s, at approximately what angular speed are the tires rotating?

Answer 1

22.3 rad/s

Further explanation

We will solve the question of uniform circular motion.

Given:

• A bicycle has tires of radius $\boxed{ \ R = 0.35 \ meters \ }$
• The bicycle is traveling at a constant speed of $\boxed{ \ v = 7.8 \ m/s \ }$

Question:

What angular speed are the tires rotating?

The Process:

Speed, angular speed, and radius are connected in the following formula:

$\boxed{\boxed{ \ v = \omega R \ }}$

The angular speed is worked out by

$\boxed{ \ \omega = \frac{v}{R} \ }$

All units are in the SI system so let us calculate the angular speed.

$\boxed{ \ \omega = \frac{7.8 \ m/s}{0.35 \ m} \ }$

Thus the value of the angular velocity of the rotating tire is $\boxed{\boxed{ \ \omega = 22.3 \ rad/s \ }}$

An additional question:

What is the frequency of tire rotation?

Recall this formula: $\boxed{ \ \omega = 2 \pi f \ } \rightarrow \boxed{ \ f = \frac{\omega}{2 \pi} \ }$

$\boxed{ \ f = \frac{22.3 \ rad/s}{2 \pi} \ }$

We get $\boxed{\boxed{ \ f = 3.55 \ Hz \ }}$

Learn more

1. Arc CD is ²/₃ of the circumference of a circle. What is the radian measure of the central angle? brainly.com/question/2115496
2. A triangle is rotated 90° about the origin brainly.com/question/2992432
3. Particle's speed and direction of motion brainly.com/question/2814900

Keywords: a bicycle has tires of radius 0.35 meters. traveling, at a constant speed of 7.8 m/s, at approximately, angular speed, the tires rotating