A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its kinetic energy?
Practice Questions
1 question
Q1
A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its kinetic energy?
(1/2)Mω^2R^2
(1/2)Iω^2
(1/2)Mω^2
Mω^2R
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.
Questions & Step-by-step Solutions
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Q
Q: A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its kinetic energy?
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.
Steps: 6
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.
