Explanation Given information: The mass of the cone as M . The height of the as h . The base radius of the cone as R . Calculation : Sketch the diagram of cone as shown in Figure 1. Consider the mass elemental disk is d m = ρ ⋅ π r 2 d z Show the expression of uniform density of cone as follows: ρ = M V (1) Here, M is the mass of cone and V is the volume of cone. Substitute 1 3 π R 2 h for V in Equation (1). ρ = M 1 3 π R 2 h Show the expression of mass of each disk as follows: d m = M d V V (2) Substitute 1 3 π R 2 h for V and π r 2 d z for d V in Equation (2). d m = M π r 2 d z 1 3 π R 2 h = 3 M R 2 h r 2 d z (3) Find the value of r using the relation: R r = h z r = R z h Substitute R z h for r in Equation (3). d m = 3 M R 2 h ( R z h ) 2 d z = 3 M R 2 h ( R 2 h 2 ) z 2 d z Show the expression of rotational moment of inertia of the element disk about the z axis. d I = 1 2 d m r 2 (4) Substitute 3 M R 2 h ( R 2 h 2 ) z 2 d z for d m and R z h for r in Equation (4)

Essential University Physics (3rd Edition)

3rd Edition

ISBN: 9780134202709

Author: Richard Wolfson

Publisher: PEARSON

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Chapter 10, Problem 73P

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To calculate: The rotational inertia of a solid.

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Chapter 10, Problem 72P

Chapter 10, Problem 74P

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Chapter 10 Solutions

Essential University Physics (3rd Edition)

Ch. 10.1 - A wheel undergoes constant angular acceleration,...Ch. 10.2 - The forces in Figs. 10.5 and 10.6 all have the...Ch. 10.3 - Would the rotational inertia of the two-mass...Ch. 10.3 - Explain why the rotational inertia of the solid...Ch. 10.3 - The figure shows two identical masses m connected...Ch. 10.4 - A wheel is rotating at 100 rpm. To spin it up to...Ch. 10.5 - The wheels of trains, subway cars, and other rail...Ch. 10 - Do all points on a rigid, rotating object have the...Ch. 10 - Prob. 2FTD Ch. 10 - Why doesnt it make sense to talk about a bodys...

Ch. 10 - Two forces act on an object, but the net force is...Ch. 10 - Is it possible to apply a counterclockwise torque...Ch. 10 - A solid sphere and a hollow sphere of the same...Ch. 10 - A solid cylinder and a hollow cylinder of the same...Ch. 10 - A circular saw lakes a long time to stop rotating...Ch. 10 - A solid sphere and a solid cube have the same...Ch. 10 - The lower part of a horses leg contains...Ch. 10 - Given a fixed amount of a material, what shape...Ch. 10 - A ball starts from rest and rolls without slipping...Ch. 10 - Exercises and Problems Exercises Section 10.1...Ch. 10 - Whats the linear speed of a point (a) on Earths...Ch. 10 - Express each of the following in radians per...Ch. 10 - A 25-cm-diameter circular saw blade spins at 3500...Ch. 10 - A compact discs rotation varies from about 200 rpm...Ch. 10 - During startup, a power plants turbine accelerates...Ch. 10 - A merry-go-round starts front rest and accelerates...Ch. 10 - Section 10.2 Torque A 320-N frictional force acts...Ch. 10 - A 110-N m torque is needed to start a revolving...Ch. 10 - A car tune-up manual calls for tightening the...Ch. 10 - A 55-g mouse runs out to the end of the 17-cm-long...Ch. 10 - You have your bicycle upside down for repairs. The...Ch. 10 - Section 10.3 Rotational Inertia and the Analog of...Ch. 10 - The shaft connecting a power plants turbine and...Ch. 10 - The chamber of a rock-tumbling machine is a hollow...Ch. 10 - A wheels diameter is 92 cm, and its rotational...Ch. 10 - Three equal masses m are located at the vertices...Ch. 10 - (a) Estimate Earths rotational inertia, assuming...Ch. 10 - A neutron star is an extremely dense, rapidly...Ch. 10 - A 108-g Frisbee is 24 cm in diameter and has half...Ch. 10 - At the MIT Magnet Laboratory, energy is stored in...Ch. 10 - Section 10.4 Rotational Energy A 25-cm-diameter...Ch. 10 - Humankind uses energy at the rate of about 16 TW....Ch. 10 - A 150-g baseball is pitched at 33 m/s spinning at...Ch. 10 - (a) Find the energy stored in the flywheel of...Ch. 10 - A solid 2.4-kg sphere is rolling at 5.0 m/s. Find...Ch. 10 - What fraction of a solid disks kinetic energy is...Ch. 10 - A rolling ball has total kinetic energy 100 J, 40...Ch. 10 - A wheel turns through 2.0 revolutions while...Ch. 10 - Youre an engineer designing kitchen appliances,...Ch. 10 - An eagle with 2.1-m wingspan flaps its wings 20...Ch. 10 - A compact disc (CD) player varies the rotation...Ch. 10 - You rev your cars engine and watch the tachometer...Ch. 10 - A circular saw spins at 5800 rpm, and its...Ch. 10 - Full-circle rotation is common in mechanical...Ch. 10 - A pulley 12 cm in diameter is free to rotate about...Ch. 10 - A square frame is made from four thin rods, each...Ch. 10 - A thick ring has inner radius 12R, outer radius R,...Ch. 10 - A uniform rectangular flat plate has mass M and...Ch. 10 - Each propeller on a King Air twin-engine airplane...Ch. 10 - The cellular motor driving the flagellum in E....Ch. 10 - Verify by direct integration Table 10.2s entry for...Ch. 10 - Prob. 55P Ch. 10 - A skaters body has rotational inertia 4.2 kgm2...Ch. 10 - A 2.4-kg block rests on a slope and is attached by...Ch. 10 - Youve got your bicycle upside down for repairs,...Ch. 10 - A potters wheel is a stone disk 90 cm in diameter...Ch. 10 - A ships anchor weighs 5.0kN. Its cable passes over...Ch. 10 - Starting from rest, a hollow ball rolls down a...Ch. 10 - A hollow ball rolls along a horizontal surface at...Ch. 10 - As an automotive engineer, youre charged with...Ch. 10 - A solid ball of mass M and radius R starts at rest...Ch. 10 - A disk of radius R has an initial mass M. Then a...Ch. 10 - A 50-kg mass is tied to a massless rope wrapped...Ch. 10 - Each wheel of a 320-kg motorcycle is 52 cm in...Ch. 10 - A solid marble starts from rest and rolls without...Ch. 10 - A disk of radius R and thickness w has a mass...Ch. 10 - The disk in Fig. 10.29 is rotating freely about a...Ch. 10 - Youre asked to check the specifications for a wind...Ch. 10 - In bicycling, each foot pushes on the pedal for...Ch. 10 - Prob. 73P Ch. 10 - A thick ring of mass M has inner radius R1 and...Ch. 10 - A thin rod of length L and mass M is free to pivot...Ch. 10 - The local historical society has asked your...Ch. 10 - Youre skeptical about a new hybrid car that stores...Ch. 10 - Figure 10.31 shows an object of mass M with one...Ch. 10 - Figure 10.32 shows an apparatus used to measure...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...

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Chapter 10 Solutions