For a composite body made of two solid cylinders of mass M1 and M2 and radius R, what is the total moment of inertia about the same axis?
Practice Questions
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Q1
For a composite body made of two solid cylinders of mass M1 and M2 and radius R, what is the total moment of inertia about the same axis?
I1 + I2
I1 - I2
I1 * I2
I1 / I2
The total moment of inertia of a composite body is the sum of the individual moments of inertia: I_total = I1 + I2.
Questions & Step-by-step Solutions
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Q
Q: For a composite body made of two solid cylinders of mass M1 and M2 and radius R, what is the total moment of inertia about the same axis?
Solution: The total moment of inertia of a composite body is the sum of the individual moments of inertia: I_total = I1 + I2.
Steps: 7
Step 1: Identify the two solid cylinders. Let's call them Cylinder 1 with mass M1 and Cylinder 2 with mass M2.
Step 2: Understand that the moment of inertia (I) for a solid cylinder about its central axis is given by the formula I = (1/2) * M * R^2, where M is the mass and R is the radius.
Step 3: Calculate the moment of inertia for Cylinder 1 using its mass M1: I1 = (1/2) * M1 * R^2.
Step 4: Calculate the moment of inertia for Cylinder 2 using its mass M2: I2 = (1/2) * M2 * R^2.
Step 5: Add the two moments of inertia together to find the total moment of inertia: I_total = I1 + I2.
Step 6: Substitute the values from Step 3 and Step 4 into the equation: I_total = (1/2) * M1 * R^2 + (1/2) * M2 * R^2.
Step 7: Factor out the common terms: I_total = (1/2) * (M1 + M2) * R^2.
