# Formula for total KE of disk rolling across table 8 m/s?

• premedonna89
In summary, the total kinetic energy of the solid disk with a mass of 5 kg and a radius of 0.9 m, rolling with a translational speed of 8 m/s, is 240. This is calculated by adding the translational and rotational kinetic energies.
premedonna89

## Homework Statement

A solid disk (mass = 5 kg, R=0.9 m) is rolling across a table with a translational speed of 8 m/s.

What is the total KE of the disk?

## Homework Equations

K = the sum of (1/2 x mass initial x velocity initial^2)

(in my textbook, there are other derivations of this formula using the variable angular velocity instead of velocity, but they yield the same answer)

## The Attempt at a Solution

KE = 1/2 x 5 kg x 8^2 = 1/2 x 5 kg x 64 = 160 (this was incorrect)

I also plugged in 80 just for the heck of it, and this was incorrect as well.

In the previous question, I was asked to find rotational KE, and I made the mistake of forgetting the coefficient (1/2) in calculating the moment of inertia. However, this KE formula does not include the moment of inertia, so this does not seem to be a problem here.

Last edited:
ugh

nevermind...its K trans + K rot = 160 + 80 = 240

The correct formula for the total KE of a rolling disk is given by:

KE = 1/2 * m * (v^2 + ω^2 * R^2)

Where m is the mass of the disk, v is the translational velocity, ω is the angular velocity, and R is the radius of the disk.

In this case, the translational velocity is 8 m/s and the angular velocity can be calculated using the relationship ω = v/R. Therefore, ω = 8/0.9 = 8.89 rad/s.

Plugging these values into the formula, we get:

KE = 1/2 * 5 kg * (8^2 + 8.89^2 * 0.9^2) = 1/2 * 5 kg * (64 + 71.53) = 1/2 * 5 kg * 135.53 = 337.825 J

Therefore, the total KE of the rolling disk is 337.825 J.

## What is the formula for calculating the total kinetic energy of a disk rolling across a table at a speed of 8 m/s?

The formula for calculating the total kinetic energy of a disk is KE = 1/2 * m * v2, where m is the mass of the disk and v is the velocity.

## What is the unit of measurement for the total kinetic energy of a disk?

The unit of measurement for the total kinetic energy of a disk is joules (J).

## Can the formula for calculating the total kinetic energy of a disk be used for other objects besides disks?

Yes, the formula can be used for any object as long as the object is in motion and has a mass and velocity.

## What happens to the total kinetic energy of a disk if its speed is doubled?

If the speed of the disk is doubled, the total kinetic energy will quadruple, as the velocity term is squared in the formula.

## Can the formula for calculating the total kinetic energy of a disk be modified for different units of measurement?

Yes, the formula can be modified to use different units of measurement, such as using kilograms for mass and meters per second for velocity. However, the final unit of measurement for kinetic energy will still be joules.

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