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

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The total kinetic energy (KE) of a solid disk rolling across a table at a speed of 8 m/s is calculated by combining translational and rotational kinetic energy. The translational KE is found using the formula K = 1/2 x mass x velocity^2, which gives 160 J for the disk's mass of 5 kg. The rotational KE is calculated using the moment of inertia, yielding an additional 80 J. Therefore, the total KE of the disk is 240 J. This confirms that both translational and rotational components must be considered in the total energy calculation.
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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:
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ugh

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

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