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

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

Options:

Correct Answer: (1/2)Iω^2

Solution:

The moment of inertia I of a disk about its axis is (1/2)MR^2. Therefore, the kinetic energy K.E. = (1/2)Iω^2 = (1/2)(1/2)MR^2ω^2 = (1/4)MR^2ω^2.

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

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

Step 1: Identify the parameters of the disk: radius (R) and mass (M).
Step 2: Understand that the disk is rotating about its axis with an angular velocity (ω).
Step 3: Recall the formula for the moment of inertia (I) of a disk about its axis, which is I = (1/2)MR^2.
Step 4: Use the formula for kinetic energy (K.E.) of a rotating object, which is K.E. = (1/2)Iω^2.
Step 5: Substitute the moment of inertia into the kinetic energy formula: K.E. = (1/2)((1/2)MR^2)ω^2.
Step 6: Simplify the equation: K.E. = (1/4)MR^2ω^2.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, calculated for a disk as (1/2)MR^2.
Rotational Kinetic Energy – The kinetic energy of a rotating object is given by the formula K.E. = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.