Finally, the boy decides that he has had enough fun. He decides to crawl to the outer edge of the merry-go-round and jump off. Somehow, he manages to jump in such a way that he hits the ground with zero velocity with respect to the ground. What is the angular speed in radians/second of the merry-go-round after the boy jumps off?
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Ответ:
Complete Question
A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.5 meters, and a mass M=211 kg. A small boy of mass m = 48 kg runs tangentially to the merry-go-round at a speed of v= 1.3 m/s, and jumps on.
Finally, the boy decides that he has had enough fun. He decides to crawl to the outer edge of the merry-go-round and jump off. Somehow, he manages to jump in such a way that he hits the ground with zero velocity with respect to the ground. What is the angular speed in radians/second of the merry-go-round after the boy jumps off?
The speed of the merry-go-round after the boy jumps off is![w_l = 0.394 \ rad/s](/tpl/images/0650/8563/504b7.png)
Explanation:
From the question we are told that
The radius of the merry-go-round is M = 211 kg
The radius is R = 1.5 meters
The mass is of the boy is m = 48 kg
The speed of the boy is![v = 1.3 \ m/s](/tpl/images/0650/8563/63fa2.png)
Generally the moment of inertia of the merry-go-round is mathematically represented as
Substituting values
The moment inertia of the boy on the merry-go-round is
Substituting values
The moment of inertia of both merry-go-round and the boy is
So![I_T = 237.38 + 108](/tpl/images/0650/8563/2fbbe.png)
Since angular momentum is conserved in that the angular momentum of the merry-go-round with the boy on it is equal to the is angular momentum of the merry-go-round without the boy on it and it is mathematically evaluated as
This can also be defined as
Where
is the angular speed of the merry-go-round
So
Making
the subject
Substituting values
From above
Where
is the angular momentum of the merry-go-round with the boy on it
And
is the angular momentum of the merry-go-round without the boy on it
So
Where
is the speed of the merry-go-round without the boy on it
Making
the subject of the formula
Ответ:
yes clash royale
Explanation: