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Chapter 5: Problem 5

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

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

Step by step solution

01

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: \(r=0.35 \mathrm{m}\)
02

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: \(ω = \cfrac{v}{r}\)
03

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: \(ω = \cfrac{9.0 \mathrm{m/s}}{0.35\mathrm{m}}\) \(ω = 25.71 \mathrm{s}^{-1}\)
04

Write the final answer

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

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Most popular questions from this chapter

A pendulum is \(0.800 \mathrm{m}\) long and the bob has a mass of 1.00 kg. When the string makes an angle of \(\theta=15.0^{\circ}\) with the vertical, the bob is moving at \(1.40 \mathrm{m} / \mathrm{s}\). Find the tangential and radial acceleration components and the tension in the string. \([\) Hint: Draw an FBD for the bob. Choose the \(x\) -axis to be tangential to the motion of the bob and the \(y\) -axis to be radial. Apply Newton's second law. \(]\)
A jogger runs counterclockwise around a path of radius \(90.0 \mathrm{m}\) at constant speed. He makes 1.00 revolution in 188.4 s. At \(t=0,\) he is heading due east. (a) What is the jogger's instantaneous velocity at $t=376.8 \mathrm{s} ?\( (b) What is his instantaneous velocity at \)t=94.2 \mathrm{s} ?$
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A high-speed dental drill is rotating at $3.14 \times 10^{4} \mathrm{rad} / \mathrm{s}$ Through how many degrees does the drill rotate in 1.00 s?
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