If a rotating object has a moment of inertia of 4 kg·m² and an angular velocity

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Question: If a rotating object has a moment of inertia of 4 kg·m² and an angular velocity of 3 rad/s, what is its kinetic energy?

Options:

Correct Answer: 12 J

Solution:

Rotational kinetic energy is given by KE = 0.5 Iω² = 0.5 * 4 kg·m² * (3 rad/s)² = 18 J.

If a rotating object has a moment of inertia of 4 kg·m² and an angular velocity of 3 rad/s, what is its kinetic energy?

If a rotating object has a moment of inertia of 4 kg·m² and an angular velocity of 3 rad/s, what is its kinetic energy?

Step 1: Identify the formula for rotational kinetic energy, which is KE = 0.5 * I * ω².
Step 2: Substitute the given moment of inertia (I = 4 kg·m²) into the formula.
Step 3: Substitute the given angular velocity (ω = 3 rad/s) into the formula.
Step 4: Calculate ω², which is (3 rad/s)² = 9 rad²/s².
Step 5: Multiply the moment of inertia by ω²: 4 kg·m² * 9 rad²/s² = 36 kg·m²·rad²/s².
Step 6: Multiply the result by 0.5: 0.5 * 36 kg·m²·rad²/s² = 18 J.
Step 7: Conclude that the kinetic energy is 18 Joules.

Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula KE = 0.5 Iω², where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia – A measure of an object's resistance to changes in its rotation, dependent on the mass distribution relative to the axis of rotation.
Angular Velocity – The rate of rotation of an object, measured in radians per second.