Chapter 4: Q.71 (page 109)

Your $64 cm$ diameter car tire is rotating at $3.5 rev / s$ when suddenly you press down hard on the accelerator. After traveling $200 m$ , the tire’s rotation has increased to $6.0 rev / s$ . What was the tire’s angular acceleration? Give your answer in $rad / s^{2}$ .

Short Answer

Expert verified

The tire’s angular acceleration is $0.75 rad / s^{2}$

Step by step solution

Given information

Diameter of car tire is $D = 64 cm$

Car tire is rotating at $ω_{i} = initial angular velocity = 3.5 rev / s$

After traveling $d = 200 m$ , the tire’s rotation has increased to $ω_{f} = final angular velocity = 6.0 rev / s$ .

We have to find the tire’s angular acceleration $α$ in $rad / s^{2}$ .

Formula

Perimeter of circle is $2 π r$

$ω_{f}^{2} = ω_{i}^{2} + 2 α ∆ θ$

Explanation

By putting values in formula

$P = 2 πr$

For radius

$r = \frac{d}{2} r = \frac{64}{2} r = 32 cm$

Putting values:

$P = 2 \times 3.14 \times 32 cm = 200.96 cm$

Converting the car tire in revolutions:

$θ = \frac{d}{P} θ = \frac{200 cm \times 100}{200.96 cm} θ = 99.52 rev$

For angular acceleration

$6^{2} = 3 . 5^{2} + 2 α \times 99.52 α = 0.1193 rev / s^{2}$

Now, convert $rev / s^{s}$ in $rad / s^{2}$

localid="1648908260302" $α = 0.1193 rev / s^{s} \times 2 π = 0.1193 rev / s^{s} \times 2 \times 3.14 α = 0.75 rad / s^{2}$

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Your $64 cm$ diameter car tire is rotating at $3.5 rev / s$ when suddenly you press down hard on the accelerator. After traveling $200 m$ , the tire’s rotation has increased to $6.0 rev / s$ . What was the tire’s angular acceleration? Give your answer in $rad / s^{2}$ .

Short Answer

Step by step solution

Given information

Formula

Explanation

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Your 64cmdiameter car tire is rotating at 3.5rev/s when suddenly you press down hard on the accelerator. After traveling 200m, the tire’s rotation has increased to 6.0rev/s. What was the tire’s angular acceleration? Give your answer in rad/s2 .

Short Answer

Step by step solution

Given information

Formula

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Torque and Rotational Motion

Nuclear Physics

Translational Dynamics

Astrophysics

Waves Physics

Study anywhere. Anytime. Across all devices.

Your $64 cm$ diameter car tire is rotating at $3.5 rev / s$ when suddenly you press down hard on the accelerator. After traveling $200 m$ , the tire’s rotation has increased to $6.0 rev / s$ . What was the tire’s angular acceleration? Give your answer in $rad / s^{2}$ .