Question

Part A 

On which of the following does the moment of inertia of an object depend? Check all that apply. 

linear speed 

linear acceleration 

angular speed 

angular acceleration 

total mass 

shape and density of the object 

location of the axis of rotation

To understand the definition and the meaning of moment of inertia; to be able to calculate the moments of inertia for a group of particles: to relate moment of inertia to kinetic energy .

Answer 1

The moment of Inertia of a point mass m located at a distance r away from the axis of rotation is I=mr²

For a system of particles, the moment of Inertia is where is the mass of the particle located at a distance from the axis of rotation.

A solid object can be considered to be made of small mass elements dm, the moment of Inertia of a solid object is the integration over these small mass elements.

where r is the distance of mass element dm from the axis of rotation. If the mass density of solid is given by ρ,

where dV is the volume of the small mass element.

Part A

The moment of Inertia of an object does not depend on linear speed, linear acceleration, angular speed, angular acceleration.

It depend on total mass, among two uniform spheres of same radius, the sphere with more total mass will have greater momentum of Inertia. So, moment of Inertia depends on total mass of an object.

As suggested by equation (1) the moment of Inertia depends on density. Also the moment of Inertia of disc of mass M and radius R is ½MR², while the moment of inertia of a ring of mass M and radius R is MR². Thus moment of Inertia depends on the shape of object.

r is the distance from the axis of rotation and moment of inertia depends on r, therefore, the moment of inertia depends on the axis of rotation. ​​​​​​

The last three options are correct.