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rjcool123 rjcool123
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12 years ago
If two objects, a uniform disk and a uniform sphere, have the same moment of inertia about their axes of rotation and the same angular velocity, then the disk has the larger rotational kinetic energy.


Why is this answer false
ok, im an idiot, its the same. Thanks
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wrote...
#1
12 years ago
I don't know...let's see

Ke= 0.5Iw^2

I1= I2
w1=w2

so why would it it be different? Unless...

the moment of inertia for a sphere
 I (sphere)=Is= (2/5) m R^2
and
I(disk)= Id= (1/2) m R^2

The total kinetic energy = Ke( traslational) +Ke(rotational)

Ke( translational) =(1/2)mV^2
since V=wR and
m(sphere)= (5/2) I /R^2
m(disk)= 2 I /R^2

Ke(translational) =(1/2)m (wR)^2

Ke(translational sphere) =[(1/2)(5/2) I /R^2](wR)^2=
Ke(translational sphere) =(5/4) I /(w)^2=

Ke(translational disk) =[(1/2)(2) I /R^2]wR)^2
Ke(translational disk) = I /(w)^2

Ke(translational sphere)/Ker(translational disk)= =(5/4) I /(w)^2 / I /(w)^2= 5/4

The linear kinetic energy will be larger for a sphere.
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