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(II) If a mass equal to half the mass of the wheel in Problem 55 is placed at the free end of the axle, what will be the precession rate now? Treat the extra mass as insignificant in size.

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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

University of Michigan - Ann Arbor

Hope College

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.

05:28

Two wheels with fixed hubs…

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02:26

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to solve this problem with Lose Equation 11.13 C for the positional angular velocity. It will be given by MGR over Iomega that AJ is now the center off moss off the combination combination off the wheel on the additional mast that this be the displaced on the axis of proficient motions. The moss it is half off. The moss off the wheel is pleased on the access off petition, so it does not contribute. D'oh! The total moment off inertia. It's a moment of inertia due to this mask about the axis of rotation in Cedo. Therefore, the total moment off inertia will still be saying on will be equal dough that off the real Ah, it is. Am I scared? As if being the one is a circle now? But we only this expression now. So let's forget about that. And let's just call the moment of inertia, the total moment of inertia equal dough, the moment of inertia after real. I. Now the addition off the moss does not change the center off Moss, but it does change the total mass that is now equal dough months off the wheel. Unless the mass that is placed on the access off rotation, which is, um, overto so the total mass is now three m over. Now let's find the sent it off, boss. So I will not be equal to. So we will use this formula for the same bet off, Boss. So m one is Thomas off the real. So that is him, x one, which is the distance off the real from the access of tradition. So that is l over to that ideas, okay. And do is the small lamb on X two for that is just and it is lent off the exits. And total mass is three m overto m one. Bless him dough as we found here. So this gives the center of mass to the equal toe do over three times. Now, we can use the seclusion to find that issue off the new positional velocity over the original or old one. New loss time. See, dimes. I knew. So this is basically our new now. Oh, large Iomega on Dhe III and Omega staying the same. So yet I have our Disick wish in now. Modest. Simplify this a cushion in Burt. So these stones cancel a we now em neurologist The total mass now is three m over too. On our on our new is this distance The news ended off months and in old is just the moss off the wheel before the small moss was added at the center. So this will be going toe just end on DDE the center off. Months off, this will be half off as we rode over here This gifts the ratio off both the positional velocities processional angular velocity is to be equally do don't. Now we can use the answer from Problem 55 to substitute for this old positional velocity that we got to be equal to eat radiant for a second in problem 55 those wars, the new position and velocity will be two times eight and so this would be 16 radian per second.

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