Rotational Energy and Kinetic Energy

[madhuparc2004]

Homework Statement

[PLAIN]http://img189.imageshack.us/img189/5994/energyq.png

Homework Equations

This is a question by Monash University...i need to do part b by Energy conservation equations...but i don;t get the answer from that..
pleasez tell me how to do part b by Energy conservation equations...
thank u

The Attempt at a Solution

 

[Mindscrape]

Do you know how to set up a Lagrangian?

 

[madhuparc2004]

Do you know how to set up a Lagrangian?

no whts that?

 

[madhuparc2004]

y is no body helping me?

 

[rdl]

Rotational energy and kinetic energy are both forms of mechanical energy, which is the energy associated with the motion and position of an object. Rotational energy specifically refers to the energy associated with the rotation of an object around an axis. This type of energy is calculated using the formula E = 1/2 Iω^2, where I is the moment of inertia and ω is the angular velocity.

Kinetic energy, on the other hand, refers to the energy an object possesses due to its motion. This type of energy is calculated using the formula E = 1/2 mv^2, where m is the mass of the object and v is its velocity.

In terms of energy conservation, the total mechanical energy of a system remains constant as long as there are no external forces acting on the system. This means that the sum of the rotational energy and kinetic energy must remain constant throughout the system's motion.

To solve part b of this question, you will need to use the conservation of energy equation: Ei = Ef, where Ei is the initial energy and Ef is the final energy. In this case, the initial energy will be the sum of the initial rotational and kinetic energies, and the final energy will be the sum of the final rotational and kinetic energies.

Since there are no external forces acting on the system, the total mechanical energy should remain constant. Therefore, you can set the initial energy equal to the final energy and solve for the final angular velocity, ωf, using the equation Ei = Ef.

Once you have found the final angular velocity, you can use the formula E = 1/2 Iω^2 to calculate the final rotational energy. Similarly, you can use the formula E = 1/2 mv^2 to calculate the final kinetic energy.

Remember to pay attention to the units of the given values and make sure they are consistent with the units in the equations. Also, be careful with the direction of rotation and velocity when calculating the final energies.