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(1I) A 4.2 -m-diameter merry-go-round is rotating frecly withan angular velocity of 0.80 rad/s. Its total moment of inertia is1760 $\mathrm{kg} \cdot \mathrm{m}^{2} .$ Four people standing on the ground, cach of mass65 $\mathrm{kg}$ suddenly step onto the edge of the merry-go-round.What is the angular velocity of the merry-go-round now? What if the people were on it initially and then jumped off in a radialdirection (relative to the merry-go-round)?

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0.48 rad $/ s$

Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

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.

02:26

(II) A 4.2-m-diameter merr…

14:42

05:28

A 4.2-m-diameter merry-go-…

02:29

(II) A 4.2 -m-diameter mer…

01:31

A 4.2 m diameter merry-go …

06:34

A disk-shaped merry-go-rou…

00:32

04:47

Eight children, each of ma…

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As seen from above, a play…

01:53

02:53

A merry-go-round has a rad…

A person of mass $75 \math…

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A person exerts a tangenti…

03:23

(II) A person of mass 75 $…

02:48

In Fig. $11-56$, a $30 \ma…

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03:18

apply the conservation of angular momentum and say that L sub one is equaling else up to this will essentially turn into the moment of inertia of one times themoment times the angular velocity, someone equaling the moment of inertia. So too times the angular velocity sub, too. Ah, we can solve, sir, for Omega sub to this would equal make us of one times, I said, one divided by ice of two. And this is equally essentially the initial angular velocity multiplied by the moment of inertia of the merry go round, divided by the moment of inertia of the merry go round, plus the moment of inertia of the added people. And so we can say that the final angular velocity would be equal to the initial angular velocity multiplied by the moment of inertia of the merry go round, divided by the moment of inertia of the merry go round, plus four people times the mass of a single person multiplied by R squared and so we can then solve Omega Sub two would be equaling. Make us up to would be equal in point 80 radiance per second. The initial angular velocity multiplied by the moment of inertia of the merry go round 1700 and 60 kilograms meters squared, divided by 1760 kilograms meters squared, plus four times the mass of a single person, 65 kilograms multiplied by 2.1 meters. Quantity squared and we find that the final angular velocity is equaling 0.48 radiance per second. If people jump off the merry go round Ah, this would be your answer for the final angular velocity. However, if people jump off the merry go round radio Lee, then they exert no torque on the mayor around and thus do not change the angular of the momentum of the merry go round. So the if they were to jump off, people jumped. Uh, radial e. We could say merry go round would continue to rotate at point 80 radiance per second. So this would be the second answer to the second part. That is the end of the solution. Thank you.

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