A solid disk of mass m1 92 kg and radius r 02 m is rotating...

A solid disk of mass m1 9.2 kg and radius R = 0.2 m is rotating with a constant angular velocity of @ = 38 rad/s. A thin rectangular rod with mass m2 3.7 kg and length L = ZR 0.4 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk: 1) What is the initial angular momentum of the rod and disk system? 2) What is the initial rotational energy of the rod and disk system?

Transcript

0:00 All right, hello.

00:01 In this question we're given this setup.

00:02 We have a spinning disk down here, and we're given its mass radius and its initial spinning speed.

00:07 And then we also have this thin rod up here, which i've drawn in blue, and this is going to fall down onto this spinning disk, and they're going to then end up spinning together.

00:16 We're going to assume that the axes is going to go through the center of this rod here, and that goes through the center of the disk.

00:23 And the reason i'm making that assumption is because the length is twice the radius, so that just seems like the reasonable thing.

00:30 And we're asked various things.

00:31 First off, what is the initial angular momentum of this system, and also what is the initial rotational energy? so i'll go ahead and do angular momentum first.

00:41 Initially, we know angular momentum is we need to have something spinning, and the only thing we have spinning in this case is this disk down here.

00:48 So we're going to have the disk, which has some moment of inertia of our disk spinning at some speed, omega naught.

00:53 Well, what is the moment of inertia of a disk spinning about its center? it is one half times the mass of that, which is m1, times the radius, so big r squared, and then that's moving at some speed, omega naught.

01:04 So i have all of these values, so i can go ahead and plug them in.

01:07 Now if i do that, rounding to two sig figs, i'm going to get 7 .0 kilogram meters per second.

01:13 That's going to be meters squared per second there.

01:16 And then i'm asked what is the initial kinetic energy? well, i know that my kinetic energy in this case is rotational, and that is going to be one half times whatever's spinning, which in this case is just the disk, times how fast it's spinning squared.

01:27 I already figured out that this is one half times m r squared times omega naught squared.

01:33 So then i can go ahead and plug in those values, and plugging that in, i get a value of 140 joules for the initial energy.

01:40 And then even though they're not stated in this question, i'm going to assume that we want to find the final angular momentum as well as the final energy...

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