A rotating object has a moment of inertia of 5 kg·m² and is rotating with an ang

A rotating object has a moment of inertia of 5 kg·m² and is rotating with an angular velocity of 4 rad/s. What is its kinetic energy? (2022)

A rotating object has a moment of inertia of 5 kg·m² and is rotating with an angular velocity of 4 rad/s. What is its kinetic energy? (2022)

Step 1: Identify the formula for rotational kinetic energy, which is KE = (1/2)Iω².
Step 2: Substitute the given values into the formula. Here, I (moment of inertia) is 5 kg·m² and ω (angular velocity) is 4 rad/s.
Step 3: Calculate ω² (4 rad/s)², which equals 16 rad²/s².
Step 4: Multiply I (5 kg·m²) by ω² (16 rad²/s²) to get 5 kg·m² * 16 rad²/s² = 80 kg·m²·rad²/s².
Step 5: Now, multiply the result by (1/2). So, (1/2) * 80 kg·m²·rad²/s² = 40 J.
Step 6: The final answer is the kinetic energy, which is 40 Joules.

Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula KE = (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.