Merry go round, rotational dynamics

In summary, a playground merry go round with a radius of 2m and moment of inertia of 250kg/m2 is initially rotating at 10rpm about a frictionless vertical axle. When a 25kg child hops onto the merry go round and sits on its edge, the new angular speed can be calculated using the equation I1w1=(I1+I2)w2, with the moment of inertia of the child treated as a point mass (I=mr2). This is because for objects other than point masses, the moment of inertia is determined by summing the moments of inertia of all the individual point masses in the object. This can be done through integrals, but for this question, treating the child as
  • #1
pb23me
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Homework Statement


A plyground merry go round of radius r=2m had a moment of inertia of I=250kg/m2 and is rotating at 10rpm about a frictionless verticle axle.Facing the axle a 25kg child hops onto the merry go round and manages to sit down on its edge.What is the new angular speed of the merry go round?


Homework Equations


I1w1=(I1+I2)w2


The Attempt at a Solution

The problem seems really easy i just plug in the values i have and get two unknowns. The only problem is i don't know what the value of I is for the child? Am i supposed to calculate this somehow? Or just use the value of I = 1/2mr2 that is for a solid cylinder?
 
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  • #2
The idea is to treat the child as a point particle.
 
  • #3
now that wouldn't be very nice:mad::biggrin:
ok but i still don't know how to obtain the value of I for the kid... is it just mr2
or do i use I that is for a solid cylinder I=1/2(mr2)?
 
  • #4
pb23me said:
now that wouldn't be very nice:mad::biggrin:
ok but i still don't know how to obtain the value of I for the kid... is it just mr2
or do i use I that is for a solid cylinder I=1/2(mr2)?
The moment of inertia of a point particle is I = mr2, so that is what you should use. Why do you think that you should use the moment of inertia of a cylinder?
 
  • #5
well, because my lab book says "The moment of inertia is given mathematically by [itex]\Sigma[/itex]mr2... so yes it seems like the moment of inertia is mr2,however when i look at all the moment of inertias for different objects solid sphere I=2/5mr2, solid cylinder 1/2mr2 and so on... where does the 2/5 and 1/2 come from? Thats why i was thinking you just can't say the moment of inertia is mr2
 
  • #6
pb23me said:
well, because my lab book says "The moment of inertia is given mathematically by [itex]\Sigma[/itex]mr2... so yes it seems like the moment of inertia is mr2,however when i look at all the moment of inertias for different objects solid sphere I=2/5mr2, solid cylinder 1/2mr2 and so on... where does the 2/5 and 1/2 come from? Thats why i was thinking you just can't say the moment of inertia is mr2
For objects other than point masses, you need to sum the moment of inertia of all the individual point masses in that object in order to determine the overall moment inertia. In practise this is done through integrals. See here for more information: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

However, for the question in hand, it is perfectly reasonable to treat the child as a point mass.
 
  • #7
ok that makes sense, thanx
 

1. What is rotational dynamics?

Rotational dynamics is the study of the movement and behavior of objects that are rotating or moving in a circular motion. It involves understanding concepts such as torque, angular velocity, and moment of inertia.

2. How does a merry go round work?

A merry go round works by converting the downward force of gravity into a horizontal force that causes the circular motion. As people push off the ground and exert a force on the merry go round, it spins faster due to the conservation of angular momentum.

3. What is the relationship between rotational dynamics and angular momentum?

Rotational dynamics is closely related to angular momentum, which is a measure of an object's tendency to continue rotating. The two are connected through the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

4. How do you calculate the moment of inertia for a merry go round?

The moment of inertia for a merry go round can be calculated using the formula I = MR², where I is the moment of inertia, M is the mass of the object, and R is the distance from the axis of rotation to the object. For a more complex object, the moment of inertia can be calculated using integration.

5. What factors affect the speed of a merry go round?

The speed of a merry go round is affected by factors such as the amount of force applied, the moment of inertia, and the friction between the ground and the merry go round. The speed can also be affected by the distribution of weight on the merry go round, as well as external factors such as air resistance.

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