Momentum Conservation of Turntable and Beetle System

In summary, the beetle travels around the edge of the turntable at an angular velocity of 0.0600 rad/s clockwise. The turntable has a mass of 80.0 g and can be treated as a uniform disk.
  • #1
amb202
2
0

Homework Statement



A beetle with a mass of 30.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 80.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0600 rad/s clockwise with respect to the turntable.


a. With respect to you, motionless as you watch the beetle and turntable, what is the angular velocity of the beetle? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise.

b. What is the angular velocity of the turntable (with respect to you)? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise.

c. If a mark is placed on the turntable at the beetle’s starting point, how long does it take the beetle to reach the mark again?


Homework Equations



L= I theta L= mvrsin

The Attempt at a Solution



I know in order to find the angular velocity of the beetle with respect to me, i need to know the angular velocity of the turntable, but without the radius, i cannot figure out how to find this.
 
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  • #2
Welcome to PF!

Hi amb202! Welcome to PF! :smile:
amb202 said:
A beetle with a mass of 30.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 80.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0600 rad/s clockwise with respect to the turntable.
…
I know in order to find the angular velocity of the beetle with respect to me, i need to know the angular velocity of the turntable, but without the radius, i cannot figure out how to find this.

Just call the radius r … you'll find it drops out in the end. :wink:
 
  • #3
But wouldn't I need the angular velocity of the turntable to figure out the velocity of the beetle with respect to me?
 
  • #4
Yes, and you can find that from the information given.

This is physics, not geometry …

you can't solve this just with geometry, you need a physical equation also …

which one do you think it is? :smile:
 

Question 1: What is the law of momentum conservation?

The law of momentum conservation states that in a closed system, the total momentum of the system remains constant. This means that the total momentum before an interaction or event is equal to the total momentum after the interaction or event.

Question 2: How does momentum conservation apply to the turntable and beetle system?

In this system, the turntable and beetle are considered a closed system because there are no external forces acting on them. This means that the total momentum of the system will remain constant, regardless of any interactions between the turntable and the beetle.

Question 3: What happens to the momentum of the turntable and beetle when they interact?

When the turntable and beetle interact, their individual momentums may change, but the total momentum of the system will remain constant. This means that if the beetle gains momentum in one direction, the turntable will gain an equal amount of momentum in the opposite direction.

Question 4: How does the mass of the objects affect momentum conservation in this system?

The mass of the objects does not affect momentum conservation in this system. This is because momentum is a vector quantity, meaning it depends on both the mass and velocity of an object. Since the turntable and beetle have equal and opposite momentums, their individual masses do not impact the total momentum of the system.

Question 5: Can momentum conservation be violated in this system?

No, momentum conservation is a fundamental law of physics and cannot be violated. In this system, as in any closed system, the total momentum will remain constant before and after any interactions or events.

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