A rolling object has a total kinetic energy of K. If it is a solid sphere, what is the translational kinetic energy?

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Q: A rolling object has a total kinetic energy of K. If it is a solid sphere, what is the translational kinetic energy?

Solution: For a solid sphere, the translational kinetic energy is K/3 of the total kinetic energy.

Steps: 9

Step 1: Understand that a rolling object has both translational and rotational kinetic energy.
Step 2: Know that the total kinetic energy (K) is the sum of translational kinetic energy (T) and rotational kinetic energy (R).
Step 3: For a solid sphere, the relationship between translational and rotational kinetic energy is specific.
Step 4: The formula for total kinetic energy for a solid sphere rolling without slipping is K = T + R.
Step 5: For a solid sphere, the rotational kinetic energy (R) is equal to (2/3)T.
Step 6: Substitute R in the total kinetic energy equation: K = T + (2/3)T.
Step 7: Combine the terms: K = (5/3)T.
Step 8: Solve for T (translational kinetic energy): T = K * (3/5).
Step 9: Since we want the translational kinetic energy in terms of K, we can also express it as K/3 of the total kinetic energy.