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

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SUMMARY

The total kinetic energy (KE) of a solid disk rolling across a table with a translational speed of 8 m/s and a mass of 5 kg is calculated using the formula K = K_trans + K_rot. The translational kinetic energy (K_trans) is determined as 160 J, while the rotational kinetic energy (K_rot) is calculated as 80 J, leading to a total KE of 240 J. The moment of inertia is not directly used in the translational KE calculation, but it is essential for determining the rotational KE.

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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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