One day after hours at a carnival a dog finds the merry-go-round. The merry-go-round is still, and the dog hops on the merry-go-round and comes face to face with a purple ride-on horse. He then walks around the edge of the merry-go-round at a constant speed to see what else is there. Eventually after some time t he winds up back at the purple horse. By what angle in degrees has the merry-go-round rotated during that time?
Details and assumptions
The mass of the dog is 20 kg.
The mass of the merry-go-round is 500 kg.
The merry-go-round can be modeled as a uniform disk of radius 8 m.
You may neglect friction.
Details and assumptions
The mass of the dog is 20 kg.
The mass of the merry-go-round is 500 kg.
The merry-go-round can be modeled as a uniform disk of radius 8 m.
You may neglect friction.
-
Let angular velocity of dog be w1 and that of the ride is w2.
By conservation of angular momentum,
1/2 * 500 * 8^2 * w2 = 20 * 8^2 * w1
So, 2*w1=25*w2
Now relative angular velocity of dog with respect to ride = w1+w2 =25/2 * w2+w2 = 27/2 * w2
In t sec., dog moves X1 angle with respect to ride and ride moves X2 angle ( with respect to ground.)
t = X1/(w1+w2) = X2/w2.
Putting X1 = 360 degrees, w1+w2 = 27/2 * w2,
X2=80/3 degrees.
By conservation of angular momentum,
1/2 * 500 * 8^2 * w2 = 20 * 8^2 * w1
So, 2*w1=25*w2
Now relative angular velocity of dog with respect to ride = w1+w2 =25/2 * w2+w2 = 27/2 * w2
In t sec., dog moves X1 angle with respect to ride and ride moves X2 angle ( with respect to ground.)
t = X1/(w1+w2) = X2/w2.
Putting X1 = 360 degrees, w1+w2 = 27/2 * w2,
X2=80/3 degrees.