Merry go round angular velocity problem asap help needed

In summary, a mass-less merry-go-round with a 4 meter diameter is initially stationary with a 30kg child at the east edge. A second child with a mass of 40kg runs north at a speed of 10km/h and jumps onto the west edge, causing the merry-go-round to turn. In order to find the magnitude of the angular velocity vector, you can use the definition of angular momentum or calculate the effective arm and use the moment of inertia. The sketches for the problem should show the direction of the linear momentum vector and the angular momentum vector.
  • #1
helpneed
7
0
A merry-go-round consists of a flat circular disk mounted on a bearing at the center allowing it to freely rotate. Consider a mass-less merry-go-round with a 4 meter diameter.
Initially a 30kg child sits at the east edge of the stationary merry-go-round. A second child with a mass of 40kg runs north at a speed of 10km/hour, jumps and lands on the west edge of the merry-go-round making it turn.
a) Make a sketch of problem during the jump when the 40kg child is in the air traveling at 10km/h north indicating the linear momentum vector (qualitatively only)
b) Make a sketch of the merry-go-round after it is turning indicating the angular momentum vector (qualitatively only)

c)Find the magnitude of the angular velocity vector of the turning merry-go-round.


I don;t expect anyone to sketch the first a and b problems
but it would help of you can tell me what what the linear momentum vector looks like.
i don't really understand the whole qualitatively part.

for c
i tried but i think i failed.

i used KE=p/2m
i got KE= 1.35 J

then used KE=IW^2/2
I=mr^2
so 1.35=((70)(2)^2)(W)/2
so W(angular velocity)= 0.00964rad/s

but I am pretty sure i am soo wrong because its asking for magnitude of the angular velocity. which is far from my thoughts.
 
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  • #2
This is not an energy-conservation problem. Energy is going to be lost. However, there are no sources of external torque in this problem, so angular momentum will be conserved.

Simply compute angular momentum of the 40kg child about merry-go-round's center right before said child grabs on. Then figure out what the angular velocity of both children together will be with that much angular momentum.

For the sketch problems, in this case, qualitatively just means they want you to show the directions of vectors. Not magnitudes.
 
  • #3
K^2 said:
This is not an energy-conservation problem. Energy is going to be lost. However, there are no sources of external torque in this problem, so angular momentum will be conserved.

Simply compute angular momentum of the 40kg child about merry-go-round's center right before said child grabs on. Then figure out what the angular velocity of both children together will be with that much angular momentum.

For the sketch problems, in this case, qualitatively just means they want you to show the directions of vectors. Not magnitudes.

so i should get the angular momentum of both the children separately and then add them together. but i don't know how i would go about doing that. with only the information given.
 
  • #4
If you draw a straight line along with a body is moving, the distance of fulcrum from that line is the effective arm. To get angular momentum, you take linear momentum and multiply it by that arm. This is easiest way to find initial angular momentum.

Alternatively, angular momentum is given by moment of inertia times angular velocity. You can use this definition to obtain angular velocity from angular momentum.
 
  • #5
K^2 said:
If you draw a straight line along with a body is moving, the distance of fulcrum from that line is the effective arm. To get angular momentum, you take linear momentum and multiply it by that arm. This is easiest way to find initial angular momentum.

Alternatively, angular momentum is given by moment of inertia times angular velocity. You can use this definition to obtain angular velocity from angular momentum.

so i should get the moment of inertia of the merry go round add it to the inertia of the two people and then divide the angular momentum by the inertia to get the magnitude of the angular velocity. okay.
 
  • #6
helpneed said:
so i should get the moment of inertia of the merry go round add it to the inertia of the two people and then divide the angular momentum by the inertia to get the magnitude of the angular velocity. okay.

The merry-go-round is massless. So what is its moment of inertia?
 

1. What is the formula for calculating angular velocity in a merry go round?

The formula for calculating angular velocity in a merry go round is ω = v/r, where ω is the angular velocity in radians per second, v is the linear velocity in meters per second, and r is the radius of the merry go round in meters.

2. How does the radius of the merry go round affect its angular velocity?

The radius of the merry go round directly affects its angular velocity. As the radius increases, the angular velocity decreases and vice versa. This is because the linear velocity is constant, but the distance traveled in one rotation (circumference) increases with a larger radius, resulting in a slower angular velocity.

3. Can you explain the difference between angular velocity and linear velocity?

Angular velocity is a measure of how quickly an object is rotating or moving in a circular path. It is measured in radians per second. Linear velocity, on the other hand, is a measure of how quickly an object is moving in a straight line. It is measured in meters per second.

4. How can I determine the direction of the angular velocity in a merry go round?

The direction of the angular velocity in a merry go round is determined by the direction of the rotation. If the merry go round is rotating clockwise, the angular velocity is considered negative. If the merry go round is rotating counterclockwise, the angular velocity is considered positive.

5. Is there a maximum angular velocity that a merry go round can reach?

Yes, there is a maximum angular velocity that a merry go round can reach. This is determined by the material and construction of the merry go round. If the angular velocity exceeds this maximum limit, the merry go round may break or become unstable.

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