A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of in
Practice Questions
Q1
A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of inertia of the flywheel is 2 kg·m², what is its rotational kinetic energy? (2020)
100 J
50 J
20 J
10 J
Questions & Step-by-Step Solutions
A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of inertia of the flywheel is 2 kg·m², what is its rotational kinetic energy? (2020)
Step 1: Identify the formula for rotational kinetic energy, which is K.E. = (1/2)Iω².
Step 2: Identify the values given in the problem: moment of inertia (I) = 2 kg·m² and angular velocity (ω) = 10 rad/s.
Step 3: Substitute the values into the formula: K.E. = (1/2)(2 kg·m²)(10 rad/s)².
Step 4: Calculate (10 rad/s)², which is 100 rad²/s².
Step 5: Multiply 2 kg·m² by 100 rad²/s² to get 200 kg·m²·rad²/s².
Step 6: Now, multiply by (1/2): (1/2)(200 kg·m²·rad²/s²) = 100 J.
Step 7: Conclude that the rotational kinetic energy of the flywheel is 100 Joules.
Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula K.E. = (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).
