f the angular velocity of a rotating wheel doubles, what happens to its rotational kinetic energy?Select one:a.It remains the sameb.It doublesc.It quadruplesd.It halves
Question
f the angular velocity of a rotating wheel doubles, what happens to its rotational kinetic energy?Select one:a.It remains the sameb.It doublesc.It quadruplesd.It halves
Solution
The rotational kinetic energy of a rotating object is given by the formula:
KE = 1/2 * I * ω^2
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
From this formula, we can see that the kinetic energy is directly proportional to the square of the angular velocity. Therefore, if the angular velocity doubles (i.e., the new angular velocity is 2ω), the new kinetic energy will be:
KE_new = 1/2 * I * (2ω)^2 = 1/2 * I * 4ω^2 = 2 * (1/2 * I * ω^2) = 2KE
So, the rotational kinetic energy quadruples. Therefore, the correct answer is c. It quadruples.
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