Question

Four point masses of 3.0 kg each are arranged in a square on masslessrods. The length of a side of the square is 0.50m. What is the rotational inertia for rotation about an axis (a) passing through masses Band C? (b) passing through masses Aand C ? (c) passing through the center of the square and perpendicular to the plane of the square?

Answer 1

Part a)

`I = 1.5 kg m^2`

Part b)

`I = 0.75 kg m^2`

Part c)

`I = 1.5 kg m^2`

Step-by-step explanation:

Part a)

Moment of inertia of the system about an axis passing through B and C is given as

`I = mL^2 + mL^2 + m(0) + m(0)`

`I = 2mL^2`

`I = 2(3 kg)(0.50^2)`

`I = 1.5 kg m^2`

Part b)

Moment of inertia of the system about an axis passing through A and C is given as

`I = m(0^2) + m((L)/(\sqrt2))^2 + m(0) + m((L)/(\sqrt2))^2`

`I = 2m(L^2)/(2)`

`I = (3 kg)(0.50^2)`

`I = 0.75 kg m^2`

Part c)

Moment of inertia of the system about an axis passing through the center of the square and perpendicular to the plane of the square

`I = m((L)/(\sqrt2))^2 + m((L)/(\sqrt2))^2 + m((L)/(\sqrt2))^2 + m((L)/(\sqrt2))^2`

`I = 4m(L^2)/(2)`

`I = 2(3 kg)(0.50^2)`

`I = 1.5 kg m^2`