A disc of radius R and mass M is rotating about its axis with an angular velocit

A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is the kinetic energy of the disc?

A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is the kinetic energy of the disc?

Correct Answer: (1/4)Mω^2R^2

Step 1: Understand that the disc is rotating, which means it has rotational kinetic energy.
Step 2: The formula for rotational kinetic energy is K = (1/2)Iω^2, where K is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
Step 3: For a disc, the moment of inertia I is given by the formula I = (1/2)MR^2, where M is the mass of the disc and R is its radius.
Step 4: Substitute the moment of inertia I into the kinetic energy formula: K = (1/2)((1/2)MR^2)ω^2.
Step 5: Simplify the equation: K = (1/4)MR^2ω^2.
Step 6: Now you have the kinetic energy of the disc in terms of its mass, radius, and angular velocity.

Rotational Kinetic Energy – The kinetic energy of an object in rotational motion is given by the formula K = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia for a Disc – The moment of inertia I for a solid disc rotating about its central axis is I = (1/2)MR^2, where M is the mass and R is the radius of the disc.