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(II) (a) What is the angular momentum of a figure skater spinning at 2.8 $\mathrm{rev} / \mathrm{s}$ with arms in close to her body, assuming her to be a uniform cylinder with a height of $1.5 \mathrm{m},$ a radius of $15 \mathrm{cm},$ and a mass of 48 $\mathrm{kg}^{2}(b)$ How muchtorque is required to slow her to a stop in 5.0 $\mathrm{s}$ , assuming she does not move her arms?

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a) $\approx 9.5 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}$b) $-1.9 \mathrm{m.N}$

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

Hope College

University of Sheffield

McMaster University

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.

04:56

( $a$ ) What is the angula…

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(II) $(a)$ What is the ang…

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05:46

Part AWhat is the angu…

02:52

A skater is initially spin…

02:05

(II) A figure skater can i…

02:03

The skater in Fig. $11.6 a…

02:12

(I) $(a)$ What is the angu…

06:14

An ice skater spinning wit…

03:29

(1) (a) What is the angula…

A figure skater can increa…

02:33

03:47

(a) Calculate the angular …

04:37

A skater spins at 2.50 rev…

01:41

so to find the angular momentum, the use a cushion 11.1. And according to that l is given by Ieave. It is moment off, Inertia times omega. Now, what is the I you? So we assume the person to be a Linda. This is not a very good diagram. So let's the that This is the bosom and it's ah repeating about this access on and they assume the bush Watson Toby the shape officer Linda on dhe for the Celinda, The moment off inertia Ah, about that access passing through the access off The Celinda is given by well, and I slept. So this is the expression off moment off inertia for the keys times omega. Now we have to convert Omega into radiant for a second now. So it's like, uh, the values likely have first also unity convert this radius in tow meters. Now Omega is given and revolutions per second and we know that one revolution ISS to buy radiance. And there we have our only got in units of Radian per second. We can solve this and we get l. A to B nine point fight K G meter squared for second now for Part B, you have to find the talk to slow down. Um, the slow, her down and such that it comes to list in the time off anytime and double or five seconds. Now this means that the final angular velocity is equal to zero. And since l is equal to times omega, it's the final. Angular momentum is also equal. Consider now we can find the dog from the definition off thought which says that dog is the weight off danger off amble a momentum with time. So del l is a left minus l eyes on Don't think is given to be five seconds. Now lf it's simply signal because the final angular momentum a zero it comes to rest now. L I t is Ah, the angular momentum that we found here And we're using this expression because the aye aye is constant because it doesn't stretch well. Oh, who's close her hands? So I even means constant because radius is constant. So this is the end. You just draw the diagram again. This is so let's say this is the person on the Celinda. We are assuming this This so on. Odd was this and this stays constant. So l A is the one that we derived here. Now we can simply like this value over here on we get dark to be negative one point mine new 10 times meter. And the negative sign here indicates that the tall is an oppose it opposite direction as the initial angular momentum.

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