Gent2324
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a metal disc X on the end of an axle rotates freely at 180 rpm. the moment of inertia of the disc is 0.034
a. find the angular momentum of the disc.

I can do part A fine, the answer is 0.064

b. after a second disc Y that is initially stationary on the same axis is engaged by X, both discs rotate at 125 revolutions per second. calculate the moment of inertia of Y.

for this i have no idea what im doing. i calculated omega, doing (125 x 60) x 2pi/60 which is 250pi. but im very confused what to do next, thanks
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mqb2766
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Part a) what are your units? I get factor of 10 different if rpm is revolutions per min.

b) Conservation of angular momentum, so the angular momentum before (one disc) is equal to the angular momentum after (two discs). You'd sum the two inertias and multiply by the new speed to get the new angular momentum and equate to the old angular momentum you've just calculated.

The new angular speed is 125 revolutions per sec? This is much faster than the original 180 rpm, which is impossible if the inertia increases. Something wrong with your units.
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Gent2324
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(Original post by mqb2766)
Part a) what are your units? I get factor of 10 different if rpm is revolutions per min.

b) Conservation of angular momentum, so the angular momentum before (one disc) is equal to the angular momentum after (two discs). You'd sum the two inertias and multiply by the new speed to get the new angular momentum and equate to the old angular momentum you've just calculated.

The new angular speed is 125 revolutions per sec? This is much faster than the original 180 rpm, which is impossible if the inertia increases. Something wrong with your units.
a. kgm^2 s^-1 i checked that the answer is correct though
b. for the angular speed that i just calculated, is that the angular speed of both or just one of them?

so the total inertia = ro from the previous question / omega which i just calculated.
and then i subtract the intertia of X to get inertia of Y?

the questions definately says rps, but im pretty sure its wrong. the answer is 0.015 so ill try and see if i can get it.

why cant the angular speed incrtease if the inertia increases?

also, how do i know that the intertia of for example a sphere is 2/5mr^2? the textbook doesnt explain it at all
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RDKGames
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(Original post by Gent2324)
why cant the angular speed incrtease if the inertia increases?
Angular speed can be expressed in terms of angular momentum L and interia I as \omega = \dfrac{L}{I}. If something in the system changes, the angular momentum is conserved so it stays the same. If I increases, then the denominator becomes bigger hence the fraction overall, and hence omega, must decrease.
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Gent2324
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(Original post by RDKGames)
Angular speed can be expressed in terms of angular momentum L and interia I as \omega = \dfrac{L}{I}. If something in the system changes, the angular momentum is conserved so it stays the same. If I increases, then the denominator becomes bigger hence the fraction overall, and hence omega, must decrease.
ah i see thanks.
since L = Iw what happens when the flywheel starts to slow down due to friction? the inertia is constant so what happens to the angular momentum? is it like dissapated as energy or something?
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RDKGames
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(Original post by Gent2324)
ah i see thanks.
since L = Iw what happens when the flywheel starts to slow down due to friction? the inertia is constant so what happens to the angular momentum? is it like dissapated as energy or something?
Friction is a non-conservative force, and so the momentum is not conserved when friction is acting on it. Since it would be slowing down, the angular velocity would get smaller, and since I stays the same, L would reduce.
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Gent2324
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(Original post by RDKGames)
Friction is a non-conservative force, and so the momentum is not conserved when friction is acting on it. Since it would be slowing down, the angular velocity would get smaller, and since I stays the same, L would reduce.
ah right ok. and do you know why a sphere is 2/5 mr^2 and not just mr^2? same goes for a disc i dont really know why they are all different
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RDKGames
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(Original post by Gent2324)
ah right ok. and do you know why a sphere is 2/5 mr^2 and not just mr^2? same goes for a disc i dont really know why they are all different
Their formulas are derived via integration which might be a slightly above A-Level for understanding, but here's the one for a disk and another for a sphere in case you want to find out anyhow:

https://www.youtube.com/watch?v=BPnbq6BobdA

https://www.youtube.com/watch?v=fbD5txXPWPw
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mqb2766
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(Original post by Gent2324)
ah right ok. and do you know why a sphere is 2/5 mr^2 and not just mr^2? same goes for a disc i dont really know why they are all different
When you think you've got an answer, post your working? The basic formula is fairly simple, but make sure the SI units are right.
If you've done linear momentum (you must have), just substitute
mass <-> inertia
speed <-> angular speed
and things should be the same.

So when momentum is maintained, adding another mass (disc) will cause the speed to drop as the product (momentum) is the same.
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Gent2324
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(Original post by mqb2766)
When you think you've got an answer, post your working? The basic formula is fairly simple, but make sure the SI units are right.
If you've done linear momentum (you must have), just substitute
mass <-> inertia
speed <-> angular speed
and things should be the same.

So when momentum is maintained, adding another mass (disc) will cause the speed to drop as the product (momentum) is the same.
assuming its rpm and the textbook made a mistake:
125 x 2pi/60 = 4.17pi rads^-1 = w
the total inertia is power / w so its 0.64/4.17pi = 0.049
0.049 = both of the inertias so its 0.049 - 0.034 = 0.015 kgm^2
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mqb2766
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(Original post by Gent2324)
assuming its rpm and the textbook made a mistake:
125 x 2pi/60 = 4.17pi rads^-1 = w
the total inertia is power / w so its 0.64/4.17pi = 0.049
0.049 = both of the inertias so its 0.049 - 0.034 = 0.015 kgm^2
Sounds about right :-)
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