A rotating object has a moment of inertia of 3 kg·m² and is rotating with an ang

A rotating object has a moment of inertia of 3 kg·m² and is rotating with an angular velocity of 10 rad/s. What is its rotational kinetic energy?

A rotating object has a moment of inertia of 3 kg·m² and is rotating with an angular velocity of 10 rad/s. What is its rotational kinetic energy?

Correct Answer: 150 J

Step 1: Identify the formula for rotational kinetic energy, which is K = (1/2)Iω².
Step 2: Identify the moment of inertia (I) given in the problem, which is 3 kg·m².
Step 3: Identify the angular velocity (ω) given in the problem, which is 10 rad/s.
Step 4: Substitute the values into the formula: K = (1/2)(3 kg·m²)(10 rad/s)².
Step 5: Calculate (10 rad/s)², which equals 100 rad²/s².
Step 6: Multiply 3 kg·m² by 100 rad²/s² to get 300 kg·m²·rad²/s².
Step 7: Multiply 300 kg·m²·rad²/s² by (1/2) to get 150 J.
Step 8: Conclude that the rotational kinetic energy is 150 J.

Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula K = (1/2)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.