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?

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Q: 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?

Solution: Kinetic energy K = (1/2)Iω^2, where I = (1/2)MR^2 for a disc.

Steps: 6

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.