If the radius of a disc is doubled while keeping its mass constant, how does its moment of inertia change?
Correct Answer: Quadrupled
- Step 1: Understand the formula for the moment of inertia of a disc, which is I = 1/2 MR^2, where M is mass and R is the radius.
- Step 2: Note that we are keeping the mass (M) constant while changing the radius (R).
- Step 3: If the radius (R) is doubled, we replace R with 2R in the formula.
- Step 4: Substitute 2R into the formula: I = 1/2 M(2R)^2.
- Step 5: Calculate (2R)^2, which equals 4R^2.
- Step 6: Now the formula looks like this: I = 1/2 M(4R^2).
- Step 7: Simplify the equation: I = 2MR^2.
- Step 8: Compare the new moment of inertia (2MR^2) with the original (1/2 MR^2).
- Step 9: Notice that the new moment of inertia is four times the original moment of inertia.
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