Question

A bicycle is moving at \(9.0 \mathrm{m} / \mathrm{s} .\) What is the angular speed of its tires if their radius is \(35 \mathrm{cm} ?\)

Short answer

Answer: The angular speed of the bicycle tires is 25.71 s^{-1}.

Step-by-step solution

Convert the radius to meters

First, let's convert the radius of the tire from centimeters to meters, since the linear speed is given in meters per second: \(r = 35 \mathrm{cm} \times \cfrac{1 \mathrm{m}}{100 \mathrm{cm}} = 0.35 \mathrm{m}\) Now, we have the radius in meters: \(r=0.35 \mathrm{m}\)

Rearrange the formula to solve for angular speed

We are given the linear speed (v) and radius (r) and need to find the angular speed (ω). We can rearrange the formula: \(v = rω\) to solve for ω: \(ω = \cfrac{v}{r}\)

Plug in the values and calculate the angular speed

Now that we have the formula to find the angular speed, we can plug in the values for the linear speed and radius: \(ω = \cfrac{9.0 \mathrm{m/s}}{0.35\mathrm{m}}\) \(ω = 25.71 \mathrm{s}^{-1}\)

Write the final answer

The angular speed of the bicycle tires is \(25.71 \mathrm{s}^{-1}\).