Explanation The cam is a solid disk of radius R that had a small disk of radius R 2 cut from it. This can be solving by use of the parallel-axis theorem. Write the expression for the moment of inertia about the rotating axis using parallel axis theorem. I d i s k = I C O M + M d i s k R 2 (I) Here, I d i s k is inertia of disk, I C O M is inertia about Centre of mass, M d i s k is mass of disk and R is the radius of disk. Write the expression for moment of inertia of the solid disk about its centre of mass. I C O M = 1 2 M d i s k R 2 Substitute 1 2 M d i s k R 2 for I C O M and R 2 for R in equation (I) and rearrange. I d i s k = 1 2 M d i s k R 2 + M d i s k ( R 2 ) 2 = 3 4 M d i s k R 2 The half radius, the cut-away small disk has one-quarter the facearea and one-quarter the volume and one-quarter the mass M d i s k of the original solid disk. Write the expression for mass of small disk. M small disk = 1 4 M disk Here, M small disk is mass of small disk. Write the expression for the moment of inertia of the small disk of radius R 2 about an axis through its centre of mass. I small disk = 1 2 M small disk ( R 2 ) 2 Here, I small disk is inertia about small disk. Substitute 1 4 M disk for M small disk in above equation and rearrange. I small disk = 1 32 M disk R 2 Subtract themoment of inertia of the small disk of radius R 2 with axis through its center. Write the expression for inertia about cam. I cam = I disk − I small disk (II) Here, I cam is inertia about cam. Substitute 3 4 M d i s k R 2 for I d i s k and 1 32 M disk R 2 for I small disk in equation (II). I cam = 3 4 M d i s k R 2 − 1 32 M disk R 2 Solve the above equation. I cam = 23 32 M disk R 2 (III) Write the expression for mass of the cam

Physics for Scientists and Engineers With Modern Physics

9th Edition

ISBN: 9781133953982

Author: SERWAY, Raymond A./

Publisher: Cengage Learning

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Chapter 10, Problem 46P

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The kinetic energy ofthe cam-shaft combination.

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Chapter 10, Problem 45P

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Physics for Scientists and Engineers With Modern Physics

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The kinetic energy ofthe cam-shaft combination.

Solution Summary: The author explains the kinetic energy of the cam-shaft combination, which can be solved by using the parallel-axis theorem.

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Chapter 10 Solutions