A rotating object has a kinetic energy of 100 J. If its angular velocity is doub

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Question: A rotating object has a kinetic energy of 100 J. If its angular velocity is doubled, what will be its new kinetic energy?

Options:

Correct Answer: 400 J

Solution:

Kinetic energy of rotation is given by KE = (1/2)Iω². If ω is doubled, KE becomes (1/2)I(2ω)² = 4(1/2)Iω² = 4KE = 400 J.

A rotating object has a kinetic energy of 100 J. If its angular velocity is doubled, what will be its new kinetic energy?

A rotating object has a kinetic energy of 100 J. If its angular velocity is doubled, what will be its new kinetic energy?

Step 1: Understand that the kinetic energy (KE) of a rotating object is calculated using the formula KE = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
Step 2: Note that the initial kinetic energy is given as 100 J.
Step 3: Recognize that if the angular velocity (ω) is doubled, it becomes 2ω.
Step 4: Substitute 2ω into the kinetic energy formula: KE = (1/2)I(2ω)².
Step 5: Simplify the equation: (2ω)² = 4ω², so KE = (1/2)I(4ω²) = 4(1/2)Iω².
Step 6: Since (1/2)Iω² is the original kinetic energy (100 J), we can replace it: KE = 4 * 100 J.
Step 7: Calculate the new kinetic energy: 4 * 100 J = 400 J.

Rotational Kinetic Energy – The formula for rotational kinetic energy is KE = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
Effect of Angular Velocity on Kinetic Energy – Doubling the angular velocity results in a quadrupling of the kinetic energy, as kinetic energy is proportional to the square of the angular velocity.