A wheel whose radius is 500 mm rotates at an angular...

A wheel whose radius is 500 mm rotates at an angular velocity of 6 rad/sec. The linear velocity of a point on the rim of the wheel is closest to: 3.0 m/s 1.5 m/s 0.3 m/s 7.5 m/s 4.5 m/s A disk with radius R= 200 m. is spinning about its center. Initially the disc has an angular velocity of 300 rev/min and is slowing down uniformly at a rate of 2.0 rad/s ². By the time it stops spinning, the total number of revolutions the disk will make is: 93 39.3 71 55 11 A truck wheel with radius R= 0.05 m has an initial angular velocity of 12 rad/s, and is slowing down at a rate of 4.0 rad/s ². How far in meters will a point on the outer rim of the wheel travel by the time it stops (no slipping). 90 m 0.9 m 36 m 9 m 18 m

Transcript

00:01 In the first question, we have a wheel whose radius is 500 millimeters.

00:08 We need to divide this by 1000 to put it into meters, and you get 0 .5 meters.

00:13 It is rotating at an angular speed of 6 radians per second, and we want to find the linear speed.

00:21 So we're going to use the equation with tangential speed, which is our linear speed, is equal to angular speed times radius.

00:27 So this is a nice equation that combines the two.

00:31 So we have 6 times 0 .5, and that gives us 3 meters per second, which is your first option from your multiple choice section.

00:42 Okay, so the next one, we have a disc, and it has a radius of 200 meters.

00:47 It is rotating initially at 300 revolutions per minute.

00:54 Put that little initial symbol there, and that is 300 revolutions per minute.

01:00 For a minute, we need to have radians per second.

01:03 So let's convert.

01:04 One revolution is the same as 2 pi radians, and these will cancel out.

01:11 One minute is the same thing as 60 seconds.

01:15 So we are going to multiply by 2 and divide by pi, and you get 31 .42 radians per second.

01:24 We're told that it is coming to a stop with an acceleration, angular acceleration, of 2 radians per second squared.

01:36 So it's slowing down.

01:37 Let me write this down real quick.

01:40 Sorry.

01:40 It is slowing down, and so if we're going to leave this as positive, we need to have the acceleration as negative because it is in the opposite direction.

01:47 Slowing down means velocity and acceleration are in opposite directions.

01:53 So we want to know how many revolutions does it pass through while it's coming to a stop.

01:57 So this is going to be one of our constant angular acceleration equations.

02:00 So i'm going to use final angular acceleration squared is equal to initial angular acceleration speed.

02:08 Excuse me.

02:08 These are angular speeds.

02:10 So final angular speed squared is equal to initial angular speed squared plus 2 times angular acceleration times angular displacement.

02:19 Subtract initial angular speed on both sides, and then divide both sides by 2 in angular acceleration.

02:28 And so that'll give us our equation.

02:30 So angular displacement is equal to our final angular speed squared minus our initial, which was that 31 .42, and that is squared, all divided by 2 times our angular acceleration.

02:48 And so when we do that, we get about 246 .7 radians, but that's not what we want...

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