/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 An ice skater rotating on fricti... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 15

An ice skater rotating on frictionless ice brings her hands into her body so that she rotates faster. Which, if any, of the conservation laws hold? a) conservation of mechanical energy and conservation of angular momentum b) conservation of mechanical energy only c) conservation of angular momentum only d) neither conservation of mechanical energy nor conservation of angular momentum

Short Answer

Expert verified
Answer: Conservation of mechanical energy and conservation of angular momentum.

Step by step solution

01

Understand the conservation of mechanical energy

Conservation of mechanical energy states that if only conservative forces are acting on a system, the total mechanical energy of the system remains constant. In this case, the ice skater is on frictionless ice, so there are no non-conservative forces (like friction or air resistance) acting on her. Thus, the mechanical energy remains constant.
02

Understand the conservation of angular momentum

The conservation of angular momentum states that the total angular momentum of a system remains constant if no external torques act upon it. In this case, the ice skater is on a frictionless surface, and no other external forces are applied, so there are no external torques. Thus, the angular momentum remains constant as well.
03

Apply the conservation laws to the ice skater's motion

The ice skater's mechanical energy and angular momentum are conserved as she brings her hands into her body, as there are no external non-conservative forces or external torques acting upon her. When she brings her hands closer to her body, her moment of inertia decreases, while her angular velocity increases, resulting in a faster spin. However, the mechanical energy remains constant as the kinetic energy of her spinning motion is not changed due to internal redistribution of mass. Similarly, the total angular momentum remains constant as the product of her moment of inertia and angular velocity remains the same.
04

Choose the correct answer

Based on the analysis in Steps 1-3, it is clear that both conservation of mechanical energy and conservation of angular momentum hold for this problem. Therefore, the correct answer is: a) conservation of mechanical energy and conservation of angular momentum

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Does a particle traveling in a straight line have an angular momentum? Explain.

A 25.0 -kg boy stands \(2.00 \mathrm{~m}\) from the center of a frictionless playground merry-go-round, which has a moment of inertia of \(200 . \mathrm{kg} \mathrm{m}^{2} .\) The boy begins to run in a circular path with a speed of \(0.600 \mathrm{~m} / \mathrm{s}\) relative to the ground. a) Calculate the angular velocity of the merry-go-round. b) Calculate the speed of the boy relative to the surface of the merry-go- round.

A CD has a mass of \(15.0 \mathrm{~g}\), an inner diameter of \(1.5 \mathrm{~cm},\) and an outer diameter of \(11.9 \mathrm{~cm} .\) Suppose you toss it, causing it to spin at a rate of 4.3 revolutions per second. a) Determine the moment of inertia of the \(\mathrm{CD}\), approximating its density as uniform. b) If your fingers were in contact with the CD for 0.25 revolutions while it was acquiring its angular velocity and applied a constant torque to it, what was the magnitude of that torque?

A round body of mass \(M\), radius \(R,\) and moment of inertia \(I\) about its center of mass is struck a sharp horizontal blow along a line at height \(h\) above its center (with \(0 \leq h \leq R,\) of course). The body rolls away without slipping immediately after being struck. Calculate the ratio \(I /\left(M R^{2}\right)\) for this body.

Two solid steel balls, one small and one large, are on an inclined plane. The large ball has a diameter twice as large as that of the small ball. Starting from rest, the two balls roll without slipping down the incline until their centers of mass are \(1 \mathrm{~m}\) below their starting positions. What is the speed of the large ball \(\left(v_{\mathrm{L}}\right)\) relative to that of the small ball \(\left(v_{\mathrm{S}}\right)\) after rolling \(1 \mathrm{~m} ?\) a) \(v_{\mathrm{L}}=4 v_{\mathrm{S}}\) d) \(v_{\mathrm{L}}=0.5 v_{\mathrm{S}}\) b) \(v_{\mathrm{L}}=2 v_{\mathrm{S}}\) e) \(v_{\mathrm{L}}=0.25 v_{\mathrm{S}}\) c) \(v_{\mathrm{L}}=v_{\mathrm{S}}\)
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Linear Momentum

Read Explanation

Particle Model of Matter

Read Explanation

Quantum Physics

Read Explanation

Translational Dynamics

Read Explanation

Work Energy and Power

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.