A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new moment of inertia?
Practice Questions
1 question
Q1
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new moment of inertia?
2I
4I
I
I/2
The moment of inertia of a disk is I = (1/2)MR^2. If the radius is doubled, the new moment of inertia becomes I' = (1/2)M(2R)^2 = 4I.
Questions & Step-by-step Solutions
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Q
Q: A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new moment of inertia?
Solution: The moment of inertia of a disk is I = (1/2)MR^2. If the radius is doubled, the new moment of inertia becomes I' = (1/2)M(2R)^2 = 4I.
Steps: 6
Step 1: Understand the formula for the moment of inertia of a disk, which is I = (1/2)MR^2, where M is the mass and R is the radius.
Step 2: Identify that the radius of the disk is being doubled. This means the new radius will be 2R.
Step 3: Substitute the new radius into the moment of inertia formula. The new moment of inertia I' will be I' = (1/2)M(2R)^2.
Step 4: Calculate (2R)^2, which equals 4R^2.
Step 5: Substitute 4R^2 back into the formula: I' = (1/2)M(4R^2).
Step 6: Simplify the equation: I' = 4 * (1/2)MR^2, which means I' = 4I, where I is the original moment of inertia.
