Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(III) Determine the $\mathrm{CM}$ of a thin, uniform, semicircular plate.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\left(0 \hat{\mathbf{i}}+\frac{4 R}{3 \pi} \hat{\mathbf{j}}\right)$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

05:08

(III) Determine the $_{CM}…

0:00

07:36

(III) A thin rod of length…

05:18

(III) A uniform circular p…

09:32

Find the centre of mass of…

14:51

Find the center of mass of…

06:56

A uniform semicircular pla…

01:29

Calculate the mass of a so…

01:24

Okay, Serving chapter in our problem. 71 here. So so, if determined, the center of massive eight, then uniforms. Semi circular, please. That's what we have here in our diagram is a semi circular plate in the X Y axes you And we should automatically see if we take the center the origin to be halfway through the plate or the center of the sport. Full circle, we could imagine Then they have the external last by symmetry as zero. Okay, so we should also know that the Y center mass We can just take the one of a total mass integrate this. Why, little d m. Okay, so now we can just rewrite what the total mass is because you know that the total mass can also be written. So we have lied Ian over in a girl tm And now if we look at in red here we have a little Oh, think of concentric rings that we have this, um, cut up by in such that of thickness of d r. What that means is we can just just think about what the mass is of each of those, right? So what we have now is a little mass of Tien. This could be written as the surface or the surface density surface mass density times the amount of area surface arrogant, that is well, we already know that That is given by Sigma Pi r d r no. Okay, so that we can just plug this stuff in. We can also see that the y coordinate the center is given by two are over pi so we can put all that stuff in now And we have the integral to our over pi sigma pi r d r Over an egg roll Sigma pi r p r So how this comes out to being too integral We have r squared d r over high in a row of r d r. And what does these all go to? Will they go from zero all the way out the full radius of the disks of 02 big R. Now let's find that insisted these were too thirds r cubed. Here we have high over too r squared here. So these they're gonna cancel out here too. I grew up. There were four. We're gonna be left with four. Pick our three. All right, that's our wife, Senator Mess Some things are Exeter, Mass. Specter here is given a zero. I, uh, plus four are over three pie jia cool.

View More Answers From This Book

Find Another Textbook

Numerade Educator