12 a dog walks at a constant angular speed of 0750 rads...

12. A dog walks at a constant angular speed of 0.750 rad/s around the circumference of a carousel that is initially at rest. The dog spots a bone on the edge of the carousel one-third of a revolution in front of him. At the instant the dog spots the bone, the carousel begins to move in the direction the dog is running, with a constant angular acceleration of 0.015 rad/s2. (a) How long will it take for the dog to catch up to the bone? (b) The dog mis5es the bone but keeps running in the same direction at the same speed. How long will it take for the dog to catch up to the bone the second time around?

Transcript

00:01 So we have a old school merry -go -round from like a park or a playground or something.

00:08 This is as seen top -down, and this is something in the middle that allows it to rotate freely.

00:16 There is a creature poorly drawn, but a creature off the merry -ground on the ground, walking at an angular velocity of 0 .750 radiance per second.

00:32 At about one third the distance away, he notices some object that's on the merry -go -round.

00:40 One -third the distance, one -third of the rotation around a circle, would be 2 pi over 3 because a full rotation is 2 -py radians.

00:49 So a third of that is 2 -5 -3.

00:50 Since we're talking about angular displacements, it's going to be the change in theta that we want to travel.

00:59 As soon as this creature sees this object and begins walking towards it, the merry -go -round begins rotating.

01:07 Starting from rest and then accelerating in the direction that the dog travels.

01:13 The creature travels with this acceleration, 0 .015 adds per second per second.

01:24 How long until this creature actually approaches the object that it sees there? we can treat this as the creature because this is all linear.

01:40 I mean it's angular, but all the relationships are linear.

01:45 So we can just treat this as the creature decelerating at this rate and then finding out how long it takes to travel that distance.

01:57 Because the object moving away at a certain acceleration or certain speed, either one, is the same as the creature slowing down with that acceleration or subtracting the new velocity from the creature.

02:13 So let's just use our delta theta is omega t plus one half alpha t squared.

02:25 And our alpha is going to be minus 0 .015...

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