Conceptual angular momentum question

[salmayoussef]

The question is:

A turtle is on a turntable. which is rotating on frictionless bearings at an angular velocity omega.
The turtle walks towards the outside of the turntable (away from the center). Which of the following is true about the system's angular velocity omega and its angular momentum (system = turntable + turtle)?

The options are:
1) The angular velocity omega decreases but the angular momentum of the system does not change.
2) The angular velocity omega does not change but the angular momentum of the system increases.
3) The angular velocity omega increases but the angular momentum of the system does not change.
4) The angular velocity omega does not change, and the angular momentum of the system does not change either.

Can someone please explain this to me? Thank you!

EDIT: I figured that the velocity of the turtle DOES increase as it walks outward, but does this change the turntable's velocity too?

 

[mrspeedybob]

Is this a homework question?

 

[salmayoussef]

Is this a homework question?

No, a conceptual question for the reading I was doing. I got it wrong, but I want to know why. It ended up being 1.

 

[mrspeedybob]

Kinetic energy is 1/2MV² where V is the magnitude of the velocity vector (AKA speed). Since energy must be conserved the speed of the turtle must be constant. If the table is rotating at 1 rev per sec with the turtle at 1 meter from the center then the turtle must have a speed of 2pi meters per sec. If the turtle walks outward to a distance of 2 meters his speed cannot change per the law of conservation of energy so he is still moving at 2pi mps but the circumference of the circle he is traveling changes from 2pi meters to 4pi meters. Since he's traveling twice as far at the same speed it takes twice as long so a revolution now takes 2 sec. Table is now rotating at 1/2 rps.

All this assumes that the mass of the table is negligible.

 

[jbriggs444]

"Frictionless beartings" says that the relevant conservation law is that of angular momentum, not kinetic energy. Kinetic energy will not be conserved in this case because there is a non-zero force in the direction of the turtle's motion.

 

[Sharath K Menon]

Umm...i think you should take into consideration the kinetic energy due to rotation.
As we are talking about the whole system, NOT the frog, the kinetic energy will be given as
KE=1/2 Iw^2
where I is the moment of inertia, w is the angular velocity.

As per the law of conservation of angular momentum, as their is NO external torque, the angular momentum is CONSTANT
When the frog moves out, the angular velocity decreases as the moment of inertia increases (I= mr^2) where r is the radius of gyration.

For a more intuitive understanding, have u ever seen ice skaters?
During spinning, they hold their hands close to their body, thus their angular velocity increases.
If they spread out their hands, angular velocity decreases, just like the frog movs outwards!

Hope this helped! :)

 

[Vibhor]

Kinetic energy will not be conserved in this case because there is a non-zero force in the direction of the turtle's motion.

Which non-zero force is acting in the direction of turtle's motion ?

 

[jbriggs444]

The turtle is "walking". This indicates a somewhat uniform speed. [By contrast, "sliding", "falling" or "rolling" might indicate otherwise]. The table is rotating. In order to maintain a somewhat uniform speed with respect to the rotating platform, there must be a centripetal force. This force will be inward. The turtle is walking outward. The work done (on the turtle) by the force will be negative. The work done (on the table) by the third law partner force will be zero. Net work done is negative. Rotational kinetic energy must decrease.

To answer your question directly: the force is that of the turtle's legs pushing inward on the turtle and outward on the turntable.

If the turtle were wearing roller skates to negate the radial force then no work would be done. Total kinetic energy would then remain constant.

Adopting an argument based on angular momentum, the same conclusion can be reached. For fixed angular momentum, kinetic energy goes down as moment of inertia goes up. Rotational kinetic energy must decrease.

 

[Vibhor]

The work done (on the turtle) by the force will be negative. The work done (on the table) by the third law partner force will be zero. Net work done is negative. Rotational kinetic energy must decrease.

To answer your question directly: the force is that of the turtle's legs pushing inward on the turtle and outward on the turntable.

The work done by force on the turtle's legs is zero as there is no displacement of the point of application .

 

[A.T.]

The work done by force on the turtle's legs is zero as there is no displacement of the point of application .

Only in the frame of the turntable. And only if you actually do model the legs in your free body diagram. If the turtle is modeled as one object, then there are no "legs", and kinetic energy is being generated/dissipated at the interface of turtle & turntable.

 

[jbriggs444]

Regardless of what frame you use, the turtle and the turntable are in relative motion. The forces on each are equal and opposite but the motions of the two are not identical in the direction of the third-law pair.