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

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Question: A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its rotational kinetic energy? (2020)

Options:

Correct Answer: (1/2)Iω²

Solution:

Rotational kinetic energy K.E. = (1/2)Iω². For a disc, I = (1/2)MR², thus K.E. = (1/4)MR²ω².

A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its rotational kinetic energy? (2020)

A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its rotational kinetic energy? (2020)

Step 1: Understand that the rotational kinetic energy (K.E.) of an object is given by the formula K.E. = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
Step 2: Identify the shape of the object. In this case, we have a disc.
Step 3: Find the moment of inertia (I) for a disc. The formula for the moment of inertia of a disc is I = (1/2)MR², where M is the mass and R is the radius of the disc.
Step 4: Substitute the moment of inertia (I) into the kinetic energy formula. So, K.E. = (1/2)((1/2)MR²)ω².
Step 5: Simplify the equation. This gives K.E. = (1/4)MR²ω².
Step 6: Conclude that the rotational kinetic energy of the disc is K.E. = (1/4)MR²ω².

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, specific to the shape and mass distribution of the object. For a disc, I = (1/2)MR².
Angular Velocity – The rate of rotation of an object, typically measured in radians per second (ω).