A rotating object has an angular velocity of 30 rad/s and a moment of inertia of

A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?

A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?

Step 1: Identify the formula for rotational kinetic energy, which is K = (1/2)Iω².
Step 2: Identify the values given in the problem: moment of inertia (I) = 3 kg·m² and angular velocity (ω) = 30 rad/s.
Step 3: Substitute the values into the formula: K = (1/2)(3 kg·m²)(30 rad/s)².
Step 4: Calculate (30 rad/s)², which is 900 rad²/s².
Step 5: Multiply 3 kg·m² by 900 rad²/s² to get 2700 kg·m²·rad²/s².
Step 6: Multiply 2700 by (1/2) to get 1350 kg·m²·rad²/s².
Step 7: The final result is K = 1350 J, which is the rotational kinetic energy.

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 (rad/s).