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A drum of 80 -mm radius is attached to a disk of 160 -mm radius. The disk and drum have a combined mass of $5 \mathrm{kg}$ and a combined radius of gyration of $120 \mathrm{mm}$. A cord is attached as shown and pulled with a force $\mathbf{P}$ of magnitude 20 N. Knowing that the coefficients of static and kinetic friction are $\mu_{s}=0.25$ and $\mu_{k}=0.2,$ respectively, determine ( $a$ ) whether or not the disk slides,(b) the angular acceleration of the disk, (c) the acceleration of $G$

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Physics 101 Mechanics

Chapter 16

Plane Motion of Rigid Bodies: Forces and Accelerations

Section 2

Constrained Plane Motion

Motion Along a Straight Line

Cornell University

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

Lectures

04:34

In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

07:57

In mathematics, a position is a point in space. The concept is abstracted from physical space, in which a position is a location given by the coordinates of a point. In physics, the term is used to describe a family of quantities which describe the configuration of a physical system in a given state. The term is also used to describe the set of possible configurations of a system.

10:33

A drum of 4 -in. radius isā¦

08:48

09:01

07:55

they start by drawing the FDD by using this and studying the problem. We know it is undergoing both translation and rotation. This means there is some off moments around the center of mass. The mass moment off inertia in this case is eyes and cultural and case kill years The equation Sigma MGI Is it going to I Therefore Sigma MGI is accorded u f a George are out. It's a gradual I, uh Therefore the defies a court Jew meu m g r out a form m gay script Also begin rate mu G out upon K square because that and will be cancelled Over here here, the home one equation and two unknown. So does all age. We are in made off one more immigration violently. If anyone is confused by effort, physical Jew, you end is a cold room. Yuji is a cultural mu engine. So here we have it done. This gin mu m g. Okay, it is because there is no reservation in the vertical direction, therefore and become G. So next we take Newton's second law in the horizontal direction. So according to that again, right, seek my FX. It's a quote to and eggs, but the summer forces are equivalent toe B minus. Anthony is it when Joe and Eggs therefore e eggs? Is it going to B minus meu m g of one? And now in the second part, another equation with two unknowns, however not he seemed to else before. So beneath make another immigration the problem straight start. No sliding is occurring, which means that they engineer a celebration at any point in the outer radius. Off the object will be the same as the does the center off months. And since we know an equation for the engine deal a salvation Big One morning Gration as follows so I can write. Okay, engine deal out. It's a question the eggs is acquired. Do I found are owned. Now combining these two equations and solving for Alfa, we can rage for eggs. Is it well, too being mine? Us mule N g a. Born And but as we know, a eggs is good too. Yeah, let's make it perfect. It is a eggs is going toe Alfa are out. So finally I can write the equation are far. Is gold do being minus mule N g of one m I owned because here, in this jumpy here, bacon is a cool tau alpha on I Grazia residents and are bank Do they know me nature? Now we have enough equations to find the solution. So we oppose it to do so by solving this system off equation so I can write again. I fight is according to meu d are out but born gays great But we know the Alfa from the above equation. So instead of file, I can rate being minus mule n g a boy and are out is go to the same term. On the right hand side is a mute g r out a horn guess group. Now let's solve this equation and write it in the form of a mule so we can get new is a quality Do be gay square a boy MGI He is great. Plus are out square now their export the values So is it weird to buy in June six by drill Hole square Born stand by 32 point do into 30 Dubai do indu it by drill square bless six by 12 square and break it complete. So the answer will be equivalent to therefore new ability equivalent to zero bank born age. Now that we find the call fission off friction mu. We move on to find the angular acceleration as shown bill so the angular acceleration can be fined with the help off the formula. Alfa is called you mut out Born Yes, Great. Now we export the values here. So it's zero brain aging in June 30 job I do into it by drill of Born six by dread Square. So down So baby, the prevailing toe 15.46 Radiant. But second, the last step is to find the horizontal acceleration, which, as we show before, can be found us. I love eggs. 30 e eggs is equal to I've ad out Now we have Alva as honest barrel, so it's good to 15.45 into age by drill, so the answer will be 10.3 Creeper Square and they can lose over Answer. The object is in rolling motion. We need three questions to solve. One is phone because there is no slipping and the other two from this song off moments. And you didn't second

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