For a composite body made of two solid cylinders of mass M1 and M2 and radius R,

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?

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?

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.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis, calculated as the sum of the products of mass and the square of the distance from the axis of rotation.
Composite Bodies – A composite body is made up of two or more individual bodies, and the total moment of inertia is found by summing the moments of inertia of each individual body.
Parallel Axis Theorem – If the axis of rotation is not through the center of mass, the parallel axis theorem may need to be applied to find the correct moment of inertia.