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A hemisphere of weight $W$ and radius $r$ is released from rest in the position shown. Determine ( $a$ ) the minimum value of $\mu_{s}$ for which the hemisphere starts to roll without sliding, $(b)$ the corresponding acceleration of point $B$. (Hint: Note that $O G=\frac{3}{8} r$ and that, by the parallelaxis theorem, $\bar{I}=\frac{2}{5} m r^{2}-m(O G)^{2}$.)

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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

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

University of Winnipeg

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.

11:45

A hemisphere of weight $W$…

01:54

A uniform solid sphere of …

04:00

A solid sphere of radius $…

11:12

A small sphere of mass $m$…

04:14

03:06

A mass $m$ of radius $r$ i…

09:58

Hello, everyone. Here it is. Given a hit me square off with the blue and really start way top Heavy spirit is the blue on radius is given art It is released from reds So omega not in zero be not zero as given position. And we have to calculate coefficient off a static friction minimum value for pure ruling wishes. And in second part, we have to Catholic Corresponding acceleration off the point given distance between Sen tried and limited. So is the medical center and center off Masses three are upon eight Now, First, we will discuss the Americans off it the filter in clock by direction with angular acceleration. Alfa, this is X coordinate off. Sent Roy already written to your by eight. This distances are Omega is given bureau initiative acceleration off a point will be acceleration off a plus acceleration off a So the expression off. All with respect to eight acceleration off a zero An acceleration off or with respect Toe able me are in Tooele Foe the words right? No acceleration off a B right? It will be so. The acceleration a We will right? That is acceleration off center off months will be acceleration off. Less acceleration off G with respect toe. So acceleration off. Oh, it's our into helper towards right and are into X. That is three are by eight or you may. Right now you may write only the X, but it will be in downward direction. So this is the question. But now we will drop free body diagram off Hammy spit. Oh, this is Jeep here. It's a big W bill act here. The reaction Push f friction push f and this will be the normal reaction center off. Must having the acceleration a x towards right on a by what's left. So I m a X having developed are into well for towards right I am a by having the value m X bar Alford towards negative by exists no culpability momento puts right about eight point. This is it. And this is the it's or make weight in tow. Expert. I am a X into our on it is rotating. So trying to help yeah, if you bring the value big is empty. I'm jean to expert. A x is m r l for in tow R plus m x bar alfa in tow. Our release operation M k squaring to help us. So from here, Alfa, you will get G X bar upon r squared plus ex body square. Let's give our respect. Give his release of violation about center off mosque se equation too. Yeah, yeah. Okay. Different commission off course along the right direction. Toby. Positive. A fiscal toe MX that is. And art elbow commission off direction positive with a long particular. But we're taking positive. You may write and minus Wait, It's called toe. I am a white, so this could be returned as any sculpture M g minus AM X bar into well for so a fiscal tamu into n this I have written wrongly Here it is. Um university f is a morale fa and we have calculated yeah, from us can be return It are alpha upon g minus expert and to help us sub serving all the values given about r is radius from equation too. We can write help for Toby G in tow. Do you buy? Eight are upon our square plus nine by 64. Our respect less okay toe by five minus nine by 64 are square. So Alfa, you will get 15 years old. All right. 56 arts from Equation three and four. New as minimum. We will get 22 98 This is one of dancing. Yeah, not be part acceleration off. We will be to our into l for Alpi it 15 g apart. 56 are so you will get 30 Gs 9.81 The acceleration off the you will get point. Just a moment. Meter per second squared or you may right 0.536 and two G direction would be what's right. That's all for it. Thanks For what?

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