Calculate the moment of inertia of a hollow sphere of mass M and radius R about
Practice Questions
Q1
Calculate the moment of inertia of a hollow sphere of mass M and radius R about an axis through its center.
2/5 MR^2
3/5 MR^2
2/3 MR^2
MR^2
Questions & Step-by-Step Solutions
Calculate the moment of inertia of a hollow sphere of mass M and radius R about an axis through its center.
Step 1: Understand what moment of inertia is. It measures how difficult it is to change the rotation of an object.
Step 2: Identify the shape of the object. In this case, we have a hollow sphere.
Step 3: Recall the formula for the moment of inertia of a hollow sphere. It is I = 2/5 MR^2.
Step 4: Identify the variables in the formula: M is the mass of the sphere, and R is the radius of the sphere.
Step 5: Plug in the values of M and R into the formula if they are given, or keep it in terms of M and R.
Step 6: Conclude that the moment of inertia of the hollow sphere about an axis through its center is I = 2/5 MR^2.
Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
Hollow Sphere – A hollow sphere is a three-dimensional object with mass distributed uniformly over its surface.
Axis of Rotation – The axis through which the moment of inertia is calculated is crucial, as it affects the distribution of mass relative to that axis.
