Help with Physics Homework Problem - A Hoop & Disk

[rubykristal]

I need help with some of my homework problems because I HARDLY understand any of this!

A hoop and a disk of the same mass and radius roll down a ramp. When they get to the bottom, they both have the same:

A) angular velocity
B) angular momentum
C) rotational kinetic energy
D) Potential energy

Any hints, please?

 

[ultimatejester]

I think its D because the gravitational potential energy would be 0 for both the objects.

A) doesn't make sense because both objects will be at rest
B)there would be no momentum since speed is 0 when they are at rest.
C)No kinetic energy because at rest
D) <---------- is the answer.

 

[Tide]

jester,

Nothing was said about them coming to rest at the bottom. They will be moving and the questions are being raised in order to compare how that energy is distributed.

ruby,

HINT: Do the two objects have the same moment of inertia?

 

[rubykristal]

Well, I know that I for the hoop is MR^2 and for the disk it's 1/2MR^2. The disk's moment of inertia is less than that of the hoop. I still have no clue ..

 

[Tide]

HINT 2: How is rotational kinetic energy related to moment of inertia?

 

[rubykristal]

RKE = (1/2)(I)(W^2)

From that... they don't have the same RKE because the moment of inertia is different for both?

 

[Tide]

Correct!

HINT 3: Energy is conserved!

 

[rubykristal]

Well, so far I know it can't be the same RKE or PE. So what's left is Angular Velocity and Angular Momentum. I'm guessing it is Angular momentum?

Because the hoop has less moment of inertia, it's angular speed increases to compensate for it ... and angular momentum is conserved?

 

[Tide]

Obviously, the angular momentum of each object is not conserved since they each start with zero angular velocity and end up with finite angular velocity. (The ramp provides torque to each of them.)

Follow HINT 3 and ...

HINT 4: The angular velocity is related to the (translational) speed by

\omega r = v

 

[Tjl]

They will have the same PE in perspective to the point from where they were let roll. Because:

PE = {mgy}

And therefor, using the top of the ramp as your 0 height. Since Potentical Energy is perspectively based, it will be the same.

 

[Doc Al]

jester,

Nothing was said about them coming to rest at the bottom. They will be moving and the questions are being raised in order to compare how that energy is distributed.

jester is correct; the PE of both will be the same (not necessarily zero).

 

[Tide]

jester is correct; the PE of both will be the same (not necessarily zero).

You missed the point. Jester rejected A, B and C for the wrong reason and I didn't want rubykristal to be misguided by erroneous logic.

 

[Doc Al]

You missed the point. Jester rejected A, B and C for the wrong reason and I didn't want rubykristal to be misguided by erroneous logic.

D'oh! You're right! (When I looked at Jester's response, I just read the first line--which was mostly correct--and the fact that he chose D. I didn't notice that he wrote his (incorrect) reasoning next to choices A, B, and C. Yikes!)

I don't care for this question (unless multiple choices are allowed) since you can answer it without knowing anything about rotational motion or inertia.