Conservation of angular momemtum

NauticaIn summary, Nautica is seeking confirmation for a problem involving a 1.8 m radius merry go round with a mass of 120 kg and an angular velocity of .5 rev/s. They are trying to determine the angular velocity after a 22 kg child gets on the edge, and have identified it as an inelastic collision with conservation of momentum. They have used the formula Iw1 + Iw2 = Iw(final) to solve for the final angular velocity, which they have determined to be 1.33 rad/s. They also clarify that the final moment of inertia is a sum of the merry-go-round's and the child's.
  • #1
nautica
Seems easy enough - but could I get a check on this.

Thanks
Nautica

A 1.8 m radius merry go round has a mass of 120 kg and is rotating with an angular velocity of .5 rev/s.

What is its angular velocity after a 22 kg childs gets on its edge which was initially at rest?

First, I determined that this was an Inelastic collision with conservation of momentum

Formula

Iw1 + Iw2 = Iw (final)

I for a disc was determined to be (1/2)MR^2

I converted the .5rev/s to 3.14rad/s

So the work is as follows:

(1/2)(120 kg * 1.8m^2)(3.14 rad/s) + 0 = ((22kg + 120 kg) * 1.8m^2)W(final)

so w(final) = 1.33 rad/s

Thanks again
Nautica
 
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  • #2
I think the equation should read
(1/2)*120 kg*(1.8m)^2*(3.14 rad/s) + 0 = ((1/2)*120 kg*(1.8m)^2 + 22 kg*(1.8m)^2)W(final)

Remember, your final I is a sum of the merry-go-round's (whose mass is distributed over a disk), and the child's (whose mass isn't.)
 
  • #3
Thanks
 

What is the conservation of angular momentum?

The conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a system remains constant in the absence of external torque. This means that in a closed system, the total amount of angular momentum before a given event must equal the total amount after.

How is angular momentum defined?

Angular momentum is a measure of the amount of rotational motion of a system, and is defined as the product of an object's moment of inertia and its angular velocity. It is a vector quantity, meaning it has both magnitude and direction.

How does conservation of angular momentum apply to real-life situations?

The conservation of angular momentum applies to many real-life situations, such as the motion of planets in the solar system, the spinning of a gyroscope, and the flight of a frisbee. It also plays a crucial role in understanding the movement of objects in space, including satellites and spacecraft.

What happens when the angular momentum of a system is not conserved?

If the angular momentum of a system is not conserved, it means that there is an external torque acting on the system. This can cause changes in the system's rotational motion, such as changes in its direction or speed. In order for angular momentum to be conserved, the net external torque on a system must be zero.

How does the conservation of angular momentum relate to other laws of physics?

The conservation of angular momentum is closely related to other fundamental laws of physics, such as the conservation of energy and the conservation of linear momentum. In fact, the conservation of angular momentum can be derived from these other laws in certain situations. It also plays a key role in many other physical principles, such as the law of universal gravitation and the equations of motion.

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