Find the center of mass of each of the following: (a) A thin wire bent into the form of a three-sided, block-shaped "u" with each segment of equal length b (b) A quadrant of a uniform circular lamina of radius b (c) The area bounded by parabola y = x2/b and the line y = b

Find the center of mass of each of the following: (a) A thin wire bent into the form of a three-sided, block-shaped "u" with each segment of equal length b (b) A quadrant of a uniform circular lamina of radius b (c) The area bounded by parabola y = x2/b and the line y = b

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 75P: Find the center of mass of a uniform thin semicircular plate of radius R. Let the origin be at the...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

Find the center of mass of each of the following:
(a) A thin wire bent into the form of a three-sided, block-shaped "u" with each segment of equal length b
(b) A quadrant of a uniform circular lamina of radius b
(c) The area bounded by parabola y = x2/b and the line y = b

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