Moments of Inertia, Kinematics, Rectilinear Motion of Particle

Question 1

What is the moment of inertia of a particle with a mass of m, a distance d from the delta axis?

Answer 1

m * d^2

Question 2

For a homogeneous solid body, what is the moment of inertia about the centre O?

Answer 2

The integral of r^2 with respect to m where m is the total mass of the body and r is the distance from the origin.

Question 3

What is the moment of inertia of a plate about the x-axis in a 2d co-ordinate system when the plate rests on the x-axis?

Answer 3

(m * h^2) / 3

Question 4

What is the moment of inertia of a plate about the x-axis in a 2d co-ordinate system when the x-axis passes through the middle of the plate?

Answer 4

(m * h^2) / 12

Question 5

What is the moment of inertia of a cylinder about the z-axis when the cylinder sits on the origin? The cylinder has a mass m and a radius R

Answer 5

(m * R^2) / 2

Question 6

What are the three ways to measure co-ordinates in a 3D space?

Answer 6

• Cartesian: x, y, z
• Polar: r, z, theta (Radius / Height / Angle)
• Spherical: r, theta, phi (Radius / Elevation Angle / Azimuth)

Question 7

How can acceleration be written as v * (dv/dx)?

Answer 7

a = dv/dt = (dv/dt) * (dx/dx) = (dv/dx) * (dx/dt) = v * dv/dx