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$\cdot$ A woman with mass 50.0 $\mathrm{kg}$ is standing on the rim of a large disk that is rotating at 0.50 $\mathrm{rev} / \mathrm{s}$ about an axis perpendicular to it through its center. The disk has a mass of 110 $\mathrm{kg}$ and a radius of 4.0 $\mathrm{m}$ . Calculate the magnitude of the total angular momentum of the woman-plus-disk system, assuming that you can treat the woman as a point.

$5.28 \times 10^{3} \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}$

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

Simon Fraser University

University of Sheffield

University of Winnipeg

McMaster University

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

04:05

A woman with mass 50 kg is…

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A woman with mass $50 \mat…

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A woman with mass 50 $\mat…

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A woman with mass 80 kg is…

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A $60.0-\mathrm{kg}$ woman…

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A 60.0-kg woman stands at …

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A horizontal platform in t…

So here the mass of the woman is 50 kilograms and then we have the angular velocity of 0.50 revolutions per second and two were going to say that this is going to be equal to pi radiance per second. Given that there are two pi radiance for everyone revolution, we can also say that the massive the turntable is 110 kilograms and that the radius is 4.0 meters. So to find the moment of inertia, this is simply the moment of inertia of the woman, plus the moment of inertia of a disc. And this will equal m r squared plus 1/2 capital m r squared. So we know that the moment of inertia will be equal to four squared times 50 the mass of the woman times half of the mass of the disc. So 55 kilograms and this is giving us 1,680 kilogram meters squared. So this would be your total moment of inertia. And then if you wanted to find the angular momentum, this will simply be the moment of inertia, times the angular velocity and this is equaling 1,680 times pi, so them the angular momentum is equalling. 5,278 kilogram meters squared per second. So this will be our angular momentum. That is the end of the solution. Thank you for watching.

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