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Derive the equation $\Sigma M_{C}=I_{\mathrm{C}} \alpha$ for the rolling disk of Fig. 16.16 where $\Sigma M_{C}$ represents the sum of the moments of the external forces about the instantaneous center $C,$ and $I_{C}$ is the moment of inertia of the disk about $C$

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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

Cornell University

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

04:34

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.

07:57

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.

01:43

Derive the equation $\Sigm…

01:31

00:59

If the disk in Fig. $17-19…

03:52

A disk of mass $m$, radius…

02:11

02:23

Find the moment of inertia…

So we start off with these two of free buddy diagrams. The moment is equal to the effective moment. We can start saying bye, you start by saying clockwise. It's positive. The some of the moments about see would be equal to the sum of the effective moments about C, and we can then substitute. This would bend the equal to the mass times acceleration of the center of mass multiplied by our plus the moment of inertia multiplied by Alfa big angular acceleration. This would then be equal to em. Our Alfa are plus men, moment of inertia multiplied by the angular acceleration. But we also know that the moment of inertia for the disk is equaling M R squared plus R. Five r And so essentially, what happens is that they cancel out, and we find that then taking clockwise to be positive. The some of the moments about C is simply equal to the moment of inertia foresee, multiplied by the angular acceleration. So essentially the moment of inertia for the center of mass cancels out. That is the end of the solution. Thank you for watching

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