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(III) Suppose a 65 -kg person stands at the edge of a 6.5 -m dia-meter merry-go-round turntable that is mounted on frictionlessbearings and has a moment of incrtia of 1850 $\mathrm{kg} \cdot \mathrm{m}^{2}$ . The tumtable is at rest initially, but when the person begins rumningat a speed of 3.8 $\mathrm{m} / \mathrm{s}$ (with respect to the tumtablc) around itsedge, the turntable begins to rotate in the opposite direction. Cakulate the angular velocity of the tumtable.

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$-0.32 \mathrm{rad} / \mathrm{s}$

Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Sheffield

University of Winnipeg

Lectures

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.

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

04:05

(III) Suppose a 65-kg pers…

0:00

A 55-kg runner runs around…

03:31

A $55 \mathrm{~kg}$ runner…

03:27

03:15

A large wooden turntable i…

02:16

A 65 kg woman stands at th…

02:06

02:29

(II) A 4.2 -m-diameter mer…

03:23

(II) A person of mass 75 $…

00:52

The turntable $T$ of a rec…

04:09

Consider again the turntab…

say here that the person speed we can say relative to the ground is gonna be, um, equaling the velocity plus visa T we're here. The V would be the person speed relative to turntable, and then this would be turned table speed relative t to the ground. And so we can then say that the turntables angular speed of the angular velocity of the turntable equals the ah turntable speed at the rim divided by the radius of the turntable itself. And so the person's angular speed relative to the ground would be equaling B plus the sub t divided by our This is equaling V over R plus the angular speed of the turntable. And so we can say that the person is to be treated as a point mass for the calculation for the moment of inertia, and we're going to apply the conservation of angular momentum. And so we can say that uh, and Elsom initial equals l final. And so we can then say zero equaling the moment of inertia of the turntable times, the angular velocity of the turntable, plus the moment of inertia for the person times the angular velocity of the person this is gonna be equaling moment of inertia for the turntable angular velocity, the turntable plus M. R squared, multiplied by the angular velocity of the turntable, plus the velocity of the person relative to the turntable divided by our. And so we can then say that the angular velocity of the turntable is going to be equal to negative m. R. V divided by i sub t plus m r squared. And at this point, we can solve. This would be negative. 65 kilograms multiplied by 3.25 meters, multiplied by 3.8 meters per second, divided by 1850 kilograms. Meters squared plus 65 kilograms multiplied by 3.25 meters wanted d squared and we find that the angular velocity of the turntable is equaling negative 0.32 radiance for a second. This negative sign. It simply means that the turntable is rotating in the opposite direction of essentially the angular velocity of the person. That is the end of the solution. Thank you

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