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A wheel of radius $r$ and centroidal radius of gyration $\bar{k}$ is released from rest on the incline and rolls without sliding. Derive an expression for the acceleration of the center of the wheel in terms of $r, \bar{k}, \beta,$ and $g$

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Physics 101 Mechanics

Chapter 16

Plane Motion of Rigid Bodies: Forces and Accelerations

Section 2

Constrained Plane Motion

Motion Along a Straight Line

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

McMaster University

Lectures

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In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

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In mathematics, a position is a point in space. The concept is abstracted from physical space, in which a position is a location given by the coordinates of a point. In physics, the term is used to describe a family of quantities which describe the configuration of a physical system in a given state. The term is also used to describe the set of possible configurations of a system.

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theory of the two free better diagrams the moment about C taking clockwise three positive. We can say them the some of the moments about see, it would be equal to the sum of the effective moments about C, and we can then substitute in can say that the weight multiplied by sine of beta multiplied by our would be equaling, then to the mass times the linear acceleration for the center of mass multiplied, multiplied by r plus the moment of inertia for the center of mass multiplied by the angular acceleration. This is gonna be equaling Then, too, whether this becomes weaken, say, m g sign of beta multiplied by our Equalling. Then the mass times are off, uh, multiplied by r plus, um K squared Alfa and we can simplify heavily saying simply, RG sign of beta would be equaling. Then two r squared plus K squared multiplied by Alfa solving for Alfa. This would then be going to RG sign of beta divided by R squared plus K squared. We know that me linear acceleration The linear acceleration for the center of mass is simply equal to the radius multiplied by the angular acceleration and so we can say that. Then the linear acceleration for the center of mass is going to be equal to R squared, multiplied by G sign of beta. And this would be divided by R squared plus K squared. That is the end of the solution. Thank you for watching.

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