Help with rotational kinetic energy, interia, etc. problem

In summary, the conversation discusses how to calculate the final linear velocity of a disc and hoop in a physics lab using conservation of energy and the work-energy theorem. It is noted that the radius and mass of the objects may cancel out and that kinematic equations may also be used. There is also a discussion about the moment of inertia for the disc and hoop and its potential impact on the calculations.
  • #1
fhwing12
1
0

Homework Statement



For a physics lab we need to calculate the final linear velocity of a disc and hoop. The only thing we are given is the length and height of the ramp and the mass and radius of the disc and hoop.

Homework Equations



I thought before that with conservation of energy, I could just set gPE = KE + KErot.

The Attempt at a Solution



It seems like all of the radius's and mass's cancel out. I had mgh = .5mv^2 + .5kmr^2(w^2) where w is omega. I then substituted in (v/r) for w and and canceled out the m's from all of the terms and ended up with gh = .5v^2 + .5kv^2. This doesn't prove to be at all helpful though because I'm nearly positive that not every disc, regardless of its mass and radius, is going to have the same final velocity. Is there some other way I can solve this problem using the work-energy theorem or something with forces? I was thinking that W = change in KE = Fx but does the KE include both linear and rotational KE? Sorry for all of the information, but thanks to anyone that responds!
 
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  • #2
fhwing12 said:
This doesn't prove to be at all helpful though because I'm nearly positive that not every disc, regardless of its mass and radius, is going to have the same final velocity.
What makes you so sure of this?

Is there some other way I can solve this problem using the work-energy theorem or something with forces? I was thinking that W = change in KE = Fx but does the KE include both linear and rotational KE? Sorry for all of the information, but thanks to anyone that responds!
Yes, KE includes linear and rotational energy. Work is actually the dot product of force times displacement, or in other words, the force times the displacement times the cosine of the angle between them.

You could probably also analyze the problem by using kinematic equations--i.e., calculate the net force and net torque, then angular acceleration and linear acceleration and use the standard equations like v = at + v_0.
 
  • #3
I'm just throwing suggestions out there (mind you I'm still in high school, but we just got finished with these concepts in my AP Physics class).

Are you completely sure that the I(moment of inertias) are the same for the disc and the hoop? If my memory doesn't fail me, I believe the I for a disc is MR^2 where as for the hoop it is 1/2MR^2.

Depending on whether I completely misunderstood what exactly you are doing in the lab, that could either be helpful or completely useless.

I hope it helps! Good luck!
 

FAQ: Help with rotational kinetic energy, interia, etc. problem

What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation around an axis. It is calculated by multiplying the moment of inertia (a measure of an object's resistance to rotation) by the square of its angular velocity.

How is the moment of inertia calculated?

The moment of inertia is calculated by summing the products of each particle's mass and its squared distance from the axis of rotation. It is a measure of an object's mass distribution and how it affects its rotational motion.

How can I determine the angular velocity of an object?

The angular velocity of an object can be determined by dividing the change in its angular displacement by the change in time. It is measured in radians per second.

What is the relationship between rotational kinetic energy and linear kinetic energy?

Rotational kinetic energy and linear kinetic energy are both forms of kinetic energy, but they are calculated differently. Rotational kinetic energy takes into account an object's moment of inertia and angular velocity, while linear kinetic energy is calculated using an object's mass and linear velocity.

How does the distribution of mass affect an object's moment of inertia?

The distribution of mass has a significant impact on an object's moment of inertia. Objects with more mass concentrated closer to the axis of rotation have a lower moment of inertia and are easier to rotate, while objects with more mass distributed far from the axis have a higher moment of inertia and are more difficult to rotate.

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