Conceptual Rotational Motion Question

[PhysicsPariah]

Homework Statement

Two objects of equal mass are on a turning wheel. Mass 1 is located at the rim of the wheel while mass 2 is located halfway between the rim and the axis of rotation. The wheel is rotating with a non-zero angular acceleration. For each of the following statements select the correct option (>, <, =) to complete the statement.

1. The moment of inertia of mass 2 about the axis of rotation is______the moment of inertia of mass 1 about the axis of rotation .

2. The tangential acceleration of mass 2 is______ the tangential acceleration of mass 1.

3. For a given time, the angle covered by mass 1 is ______ the angle covered by mass 2.

4. The magnitude of the total acceleration of mass 1 is ____ the total acceleration of mass 2.

5. The speed of mass 1 is ____ the speed of mass 2.

6. The angular acceleration of mass 1 is _____ the angular acceleration of mass 2.

7. The centripetal (radial) acceleration of mass 1 is______the centripetal acceleration of mass 2.

8. For a given time, mass 1 travels a distance that is______the distance traveled by mass 2.

Homework Equations

[itex]I=mr^2[/itex]
[itex]S=R\theta[/itex]
[itex]\alpha=\Delta w/ \Delta t[/itex]

The Attempt at a Solution

1. Less than (because they have the same mass, the bigger radius means bigger inertia)
2. Less than (smaller radius means smaller accel)
3. Equal to (angle should be the same regardless of radius)
4. Less than
5. Equal to
6. Equal to
7. Less than (bigger radius means smaller accel)
8. Greater than (mass 1 along the edge should travel a farther distance than mass 2 closer to the axis)

I'm really having problems with this problem. Its an online system and it doesn't tell me which are wrong so any help would be greatly appreciated.
PS. Sorry if I mess up the latex writing, I tried really hard to get it right

 

[Doc Al]

7. Less than (bigger radius means smaller accel)

Why do you say "bigger radius means smaller acceleration"?

You got three wrong (by my count), but I can only comment on ones for which you gave your reasoning.

 

[PhysicsPariah]

Hmm I had to go back to the definition of centripetal acceleration and I found my mistake. I didn't realize it was the rate of change of tangential velocity times radius squared. As for the other 3, I believe is correct because angular acceleration is the same in both (because t is the same and [itex] \theta [/itex] is the same for both masses.) Speed, again, I went back to the basic definition of distance traveled over time, m1 traveled more so I'm going to say greater than. Number 4 was perhaps the trickiest for me because we never looked at acceleration as a magnitude in class. Could somebody please explain how that works? or how to calculate |total accel|. ? I'm very interested.

 

[Doc Al]

Hmm I had to go back to the definition of centripetal acceleration and I found my mistake. I didn't realize it was the rate of change of tangential velocity times radius squared.

The centripetal acceleration [itex]= v^2/r = \omega^2r[/itex].

As for the other 3, I believe is correct because angular acceleration is the same in both (because t is the same and [itex] \theta [/itex] is the same for both masses.) Speed, again, I went back to the basic definition of distance traveled over time, m1 traveled more so I'm going to say greater than.

Good.

Number 4 was perhaps the trickiest for me because we never looked at acceleration as a magnitude in class. Could somebody please explain how that works? or how to calculate |total accel|. ? I'm very interested.

The acceleration has two perpendicular components: Tangential and Radial. Combine them (like any other vector) to get the total.

 

[PhysicsPariah]

http://theory.uwinnipeg.ca/physics/circ/node6.html
Thats where I got my centripetal force information.

And according to what you said, number 4 should be greater than.
Thanks a lot Doc Al. I really appreciate it.