Merry go round, rotational dynamics

[pb23me]

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 vertical 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?

 

[Hootenanny]

The idea is to treat the child as a point particle.

 

[pb23me]

now that wouldn't be very nice
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)?

 

[Hootenanny]

now that wouldn't be very nice
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?

 

[pb23me]

well, because my lab book says "The moment of inertia is given mathematically by $\Sigma$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

 

[Hootenanny]

well, because my lab book says "The moment of inertia is given mathematically by $\Sigma$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.

 

[pb23me]

ok that makes sense, thanx