Converting tangential momentum to angular momentum

In summary, when a person jumps onto a merry-go-round, their linear momentum is transferred to the Earth through the merry-go-round as it exerts a force towards its center. This means that overall, linear momentum is conserved, but if you only consider the person and the merry-go-round, it is not. To convert their linear momentum to angular momentum, you can use the formula L = IW, where I is the moment of inertia and W is the angular speed. The moment of inertia for a point mass can be calculated by multiplying the mass of the person by the square of the distance from the center. By multiplying I and W, you can calculate the angular momentum of the person on the merry-go-round.
  • #1
jforce93
26
0
"converting" tangential momentum to angular momentum

If someone is running and jumps onto a merry-go-round, momentum is still conserved, correct? (ignoring friction). So, would the momentum of the person while they were running be the same as the angular momentum of the merry-go-round after they jumped onto it? If not, how would I "convert" (for lack of a better term) their momentum into angular momentum? I know about

L = IW
and all, but I am really confused.

Thanks,

Jordan
 
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  • #2


For simplicity's sake assume that the merry-go-round has no mass and therefore possesses no momentum of its own and the person's speed is the same before he or she jumps on (when they are running) and after (when they are sitting on the merry-go-round). Also assume no friction and that the person is a "point" mass (again just for simplicity).

Linear momentum is conserved, but in this case the person's momentum is transferred to the Earth through the merry-go-round as the merry-go-round exerts a force on the person towards its center. In other words, linear momentum is covered overall (if you include the Earth) but if you only include the person and the merry-go-round in your system then linear momentum is NOT conserved. Note the magnitude of the person's linear momentum stays the same since the person continues to travel at the same speed, but the momentum changes since momentum is a vector quantity and the person's direction is continually changing as they go around the merry-go-round.

To convert, just get the person's speed before the jump and combine that with the distance from the center to come up with the omega (the W, angular speed) value. So for example if the person is going 15 ft per second and is 5 feet from the center of the merry-go-round, they are doing speed (ft/sec) / circumference (ft/revolution) = 15/(2*5*pi) revolutions/sec = .477 rev/sec = 3 radians/sec (I'm not sure if my math is right, but you get the idea).

To get I:http://en.wikipedia.org/wiki/List_of_moments_of_inertia"

use the one for point mass (m*r*r) so you get mass of person * 5 * 5

multiply I and W together to get angular momentum! Note that this problem might be doable if you are not given the mass of the person, set it up and see if the m's cancel. Good luck!
 
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Related to Converting tangential momentum to angular momentum

1. What is the difference between tangential momentum and angular momentum?

Tangential momentum is a measure of the linear motion of an object, while angular momentum is a measure of the rotational motion of an object.

2. How can tangential momentum be converted to angular momentum?

Tangential momentum can be converted to angular momentum by multiplying it by the distance from the point of rotation.

3. What is the relationship between tangential momentum and angular velocity?

The relationship between tangential momentum and angular velocity is that they are directly proportional. As tangential momentum increases, angular velocity also increases.

4. How does converting tangential momentum to angular momentum affect the rotational motion of an object?

Converting tangential momentum to angular momentum increases the rotational motion of an object. This is because angular momentum is a measure of an object's rotational speed and mass.

5. Can tangential momentum be converted to angular momentum for all types of motion?

No, tangential momentum can only be converted to angular momentum for rotational motion. For linear motion, tangential momentum and angular momentum are equivalent.

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