Falling stick problem (no friction): What is the kinetic energy?

• phos19
In summary, the conversation discusses the calculation of kinetic energy for a falling stick with no friction, assuming no energy dissipation. The suggested equation for kinetic energy includes both rotational and translational components, and the person asking for help is advised to provide a clear statement of the problem or specific question.
phos19
Since there is no friction : $$m \ddot{x} = 0$$ (no x motion).For the kinetic energy , I've tried: $$K = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m v^2_cm = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m \dot{z}^2$$ . Giving me a weird expression , shouldn't the kinetic energy just be half the the moment of inertia about the contact point times $$\dot{\alpha}^2$$?

K.E would be sum of rotational and translational kinetic energy. Gravity is a conservative force, and if there's no air resistance and assuming that no energy dissipation happens due to heat and sound etc, then K.E of falling stick = Rotational K.E about it's Center of mass + Translational K.E of the center of mass.

MatinSAR

1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is a scalar quantity and is dependent on the mass and velocity of the object.

2. How is kinetic energy related to the falling stick problem with no friction?

In the falling stick problem with no friction, the stick is only affected by the force of gravity. As the stick falls, its potential energy is converted into kinetic energy. This means that the stick's kinetic energy increases as it falls towards the ground.

3. What is the formula for calculating kinetic energy?

The formula for calculating kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

4. How does the mass and velocity of an object affect its kinetic energy?

The mass and velocity of an object have a direct relationship with its kinetic energy. As the mass or velocity increases, the kinetic energy also increases. This means that a heavier object or an object with a higher velocity will have more kinetic energy than a lighter object or an object with a lower velocity.

5. Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy, such as potential energy, thermal energy, or sound energy. This conversion usually occurs when the object collides with another object or when it comes to a stop due to friction or other forces.

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