Chapter 10: Q15P (page 288)

Starting from rest, a wheel has constant acceleration $α = 3.0 \frac{rad}{s^{2}}$ . During a certain role="math" localid="1660898447415" $4.0 s$ interval, it turns through $120 rad$ . How much time did it take to reach that $4.0 s$ interval?

Short Answer

Expert verified

Wheel requires $8.0 s$ time to reach that interval.

Step by step solution

Listing the given quantities

The angular acceleration of a wheel, $α = 3.0 \frac{rad}{s^{2}}$

The time interval of $120 rad$ displacement is, $t = 4.0 s$

The angular displacement is, $θ = 120 rad$

Understanding the kinematic equations

Use the kinematic equation for constant angular acceleration to calculate the initial angular velocity of the given interval. Use angular velocity formula to determinethefinal angular velocity asthewheel starts from rest.

Formula:

i) $ω = ω_{0} + αt$

ii) $θ = ω_{0} t + \frac{1}{2} {αt}^{2}$

Calculate the angular velocity

The kinematic equation for angular motion is:

$θ = ω_{0} t + \frac{1}{2} α t^{2}$

Substitute the value and solve as:

Solving for $ω_{0}$ :

$ω_{0} = 24 \frac{rad}{s}$

Calculate the time required for the wheel to get the angular speed of 24 rads

Consider the expression for the angular speed as:

$ω = ω_{0} + αt$

Solving for time, $t = T$

$T = \frac{ω - ω_{0}}{α}$

Substitute the values and solve as:

$\begin{matrix} T = \frac{24 - 0}{3.0} \\ = 8.0 s \end{matrix}$

Time required for the wheel is $8.0 s$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Starting from rest, a wheel has constant acceleration $α = 3.0 \frac{rad}{s^{2}}$ . During a certain role="math" localid="1660898447415" $4.0 s$ interval, it turns through $120 rad$ . How much time did it take to reach that $4.0 s$ interval?

Short Answer

Step by step solution

Listing the given quantities

Understanding the kinematic equations

Calculate the angular velocity

Calculate the time required for the wheel to get the angular speed of 24 rads

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Electricity and Magnetism

Electrostatics

Wave Optics

Further Mechanics and Thermal Physics

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

Starting from rest, a wheel has constant acceleration α=3.0rads2. During a certain role="math" localid="1660898447415" 4.0sinterval, it turns through120rad. How much time did it take to reach that 4.0s interval?

Short Answer

Step by step solution

Listing the given quantities

Understanding the kinematic equations

Calculate the angular velocity

Calculate the time required for the wheel to get the angular speed of 24 rads

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Electricity and Magnetism

Electrostatics

Wave Optics

Further Mechanics and Thermal Physics

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

Starting from rest, a wheel has constant acceleration $α = 3.0 \frac{rad}{s^{2}}$ . During a certain role="math" localid="1660898447415" $4.0 s$ interval, it turns through $120 rad$ . How much time did it take to reach that $4.0 s$ interval?