Rotational kinetic energy of a disk

In summary, to find the kinetic energy of the weight at a given time or distance fallen from the disk, one must determine the velocity of the mass as a function of time or distance traveled. This depends on the situation when the disk is dropped and mass is released, as well as the difference in velocity between the mass and the rotational axis of the disk. The acceleration of the mass is limited by the local acceleration due to gravity.
  • #1
physgirl
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ok, so a thread with hanging mass at the end is wrapped around a disk. the disk is dropped and mass is released. how do you find the kinetic energy of the weight at a given time/distance fallen from the disk? I'm not sure to whether use rotational kinetic energy or linear kinetic energy... all the basic values are given, except for the moment of inertia of the disk... so how would I find the kinetic energy of the mass at a given time after its release?
 
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  • #2
It depends on the what happens when "the disk is dropped and mass is released."

If the disk and mass are dropped together, they are both subject to the same acceleration, g, unless there is more air resistance (force) on the disc.

Obviously, the kinetic energy of the mass if given by 1/2mv2, so one must determine the velocity of the mass as a function of time or distance traveled.

If the mass is moving relative to the disk, then one would need to determine the difference in velocity (speed) of the mass with respect to the rotational axis of the disk, and this speed difference would be manifest in the rotation of the disk, and the differential speed would be related to the angular velocity of the disk.

Note - the acceleration of any mass in 'freefall' is limited by the local acceleration due to gravity.
 
  • #3


To find the kinetic energy of the weight at a given time/distance fallen from the disk, you will need to use both rotational and linear kinetic energy equations. First, you will need to determine the moment of inertia of the disk, which is a measure of its resistance to rotational motion. This can be calculated using the mass and radius of the disk, as well as its shape and distribution of mass. Once you have the moment of inertia, you can use the rotational kinetic energy equation, which is ½Iω^2, where I is the moment of inertia and ω is the angular velocity of the disk.

Next, you will need to consider the linear motion of the weight as it falls from the disk. This can be calculated using the linear kinetic energy equation, which is ½mv^2, where m is the mass of the weight and v is its velocity. To determine the velocity, you will need to use the equation for conservation of energy, which states that the total energy of the system (rotational and linear) remains constant. This means that the initial potential energy of the weight at the top of the disk will be equal to the sum of its rotational and linear kinetic energies at any given time/distance fallen from the disk.

In summary, to find the kinetic energy of the weight at a given time/distance fallen from the disk, you will need to calculate the moment of inertia of the disk, use the rotational kinetic energy equation, and consider the linear motion of the weight using the conservation of energy principle.
 

1. What is rotational kinetic energy?

Rotational kinetic energy is the energy possessed by an object due to its rotation around an axis. It is a form of kinetic energy that is associated with an object's rotational motion.

2. How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is: KE = 1/2 * I * ω^2, where KE is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.

3. What is the relationship between rotational kinetic energy and mass?

The amount of rotational kinetic energy an object has is directly proportional to its mass. This means that the more mass an object has, the more rotational kinetic energy it will have.

4. How does the radius of a disk affect its rotational kinetic energy?

The radius of a disk affects its moment of inertia, which in turn affects its rotational kinetic energy. The larger the radius, the larger the moment of inertia, and therefore the more rotational kinetic energy the disk will have.

5. Is rotational kinetic energy the same as linear kinetic energy?

No, rotational kinetic energy and linear kinetic energy are two different forms of kinetic energy. Rotational kinetic energy is associated with an object's rotation, while linear kinetic energy is associated with an object's linear motion.

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