# Rotational Collision: Mass, Radius & KE Lost

• huskydc
In summary, two disks with masses M1 = 350 g and M2 = 247 g, and radii R1 = 10 cm and R2 = 5 cm, respectively, were rotating at different initial speeds (f(initial) = 152 rpm and not rotating) when they were brought into contact and frictional forces acted to bring them to a common rotational speed (f(final) = 129.2 rpm). The problem then asked for the amount of kinetic energy lost due to friction, which was calculated by subtracting the initial kinetic energy from the final kinetic energy using the given equations for rotational kinetic energy. The mistake in the calculation was originally assuming the moment of inertia (I) to be 3/2 *

#### huskydc

A disk of mass M1 = 350 g and radius R1 = 10 cm rotates about its symmetry axis at finitial = 152 rpm. A second disk of mass M2 = 247 g and radius R2 = 5 cm, initially not rotating, is dropped on top of the first. Frictional forces act to bring the two disks to a common rotational speed f(final).

I already found f(final) to 129.2 rpm.

next the problem ask for the amount of Kinetic energy lost due to friction.

so i subtract initial KE from final KE to get the change in KE.

did i approach this wrong? b/c i kept getting the wrong answers...and all the numbers i got were pretty big...

Looks OK. Show how you calculated the KE.

The two masses rotate, when in final contact, at different angular velocities.

You didn't use the same (common) angular velocity for both , did you?

but it says that friction brings the two disks to a common rotational speed final. shouldn't i be using the same though?

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huskydc said:
but it says that friction brings the two disks to a common rotational speed final. shouldn't i be using the same though?
For the final KE, of course you should use a common rotational speed (which you've already calculated). And for the initial KE, you would use the given initial rotational speed.

Again: How did you calculate the rotational KE of the disks? (Be sure to use $\omega$ in radians/sec, not rpm.)

hold on...it says it's rotating about its symmetry axis, doesn't that make I = 3/2 m r^2?

anyways...if we assume I to be .5 m r^2, i calculate the KE like this:

KE initial = .5 I(1) omega(initial)^2 + .5 I(2) omega(initial)^2
= .5 [.5 m(1) r(1)^2] omega(initial)^2
= .25 m(1) r(1)^2 omega(initial)^2

KE final = .5 I(1) omega(final)^2 + .5 I(2) omega(final)^2
= .25 m(1) r(1)^2 omega(final)^2 + .25 m(1) r(1)^2 omega(final)^2

KE final - KE initial =...

convert rpm to rad/s...and plug in numbers...i get a range of different numbers, big to small..

huskydc said:
hold on...it says it's rotating about its symmetry axis, doesn't that make I = 3/2 m r^2?
No. For a disk, $I = 1/2 M R^2$.

anyways...if we assume I to be .5 m r^2, i calculate the KE like this:

KE initial = .5 I(1) omega(initial)^2 + .5 I(2) omega(initial)^2
= .5 [.5 m(1) r(1)^2] omega(initial)^2
= .25 m(1) r(1)^2 omega(initial)^2
Nothing wrong with this.

KE final = .5 I(1) omega(final)^2 + .5 I(2) omega(final)^2
= .25 m(1) r(1)^2 omega(final)^2 + .25 m(1) r(1)^2 omega(final)^2
I assume you meant the second term to be for the second disk: m(2), r(2).

KE final - KE initial =...

convert rpm to rad/s...and plug in numbers...i get a range of different numbers, big to small..
Looks OK to me. How can one method give you a range of answers?

huskydc said:
but it says that friction brings the two disks to a common rotational speed final. shouldn't i be using the same though?
OK, I think I figured this out.

huskydc said:
...
Frictional forces act to bring the two disks to a common rotational speed f(final).

..
When I first read this, I interpreted it as meaning that when the two disks came into contact then (kinetic) friction between the disks would start to rotate the disk M2 until the two disks had the same periferal velocity. (At which point rolling friction would take over.) Had that been the case, then ω2 = 2*ω1. I thought the "rotational" bit must be a typo!

Hiowever it seems that in addition to the kinetic friction between the disks, there is also some (internal) friction slowing disk2 down until ω2 = ω1.

My mistake - sorry 'bout that.