Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q. 38 (page 107)

38. II FIGURE EX4.38 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?

Short Answer

Expert verified

The number of revolution made by a particle moving in a circle during the first 4s is 9.55 rev.

Step by step solution

01

Step 1. Given information

From the graph up to t =2s the particle is having angular acceleration and from time t = 4s the particle is having constant angular velocity.

Then for t=2s

α2=dωdt=20rad/s−02s=10rad/s2

02

Step 2. Explanation

Initial angular velocity is

ω0=0rad/s

ThenΔθ2=ω0t+12α2t2=0+1210rad/s2(2s)2=20rad

Now from t=2sto t=4s,ω=20rad/s

Then

role="math" localid="1652331307170" Δθ4=ωΔt=(20rad/s)2s=40rad

Then total angular displacement is

Δθ=ΔθL+Δθ4=20rad+40rad=60rad

Now we know thatΔθ=2πN

Thus number of revolutions is

N=Δθ2π=60rad2πrad/rev=9.55rev

Therefore, the number of revolutions made by a particle moving in a circle during the first 4s is 9.55 rev.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30sto speed up from rest to its top speed of 1rotation every 1.3s. The astronaut is strapped into a seat 6.0mfrom the axis.

a. What is the astronaut’s tangential acceleration during the first 30s?

b. How many g’s of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.8m/s2of acceleration is1g.

A cart that is rolling at constant velocity on a level table fires a ball straight up.

a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or directly in the tube? Explain.

b. Will your answer change if the cart is accelerating in the forward direction? If so, how?

Problems 1 and 2 show a partial motion diagram. For each:

a. Complete the motion diagram by adding acceleration vectors.

b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don't forget to include enough information to make the problem completely and to state clearly what is to be found.

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 60 m away, making a 3.0° angle with the ground. How fast was the arrow shot?

15. FIGURE Q4.15 shows a pendulum at one end point of its arc.

a. At this point, ωis positive, negative, or zero? Explain.

b. At this point, αis positive, negative, or zero? Explain.

FIGURE Q4.15
See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Dynamics

Read Explanation

Wave Optics

Read Explanation

Fields in Physics

Read Explanation

Medical Physics

Read Explanation

Electromagnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free