Question

A 1 m diameter wagon wheel consists of a thin rim having a mass of 4 kg and six spokes, each with a mass of 1.5 kg. Find the moment of inertia of the wagon wheel for rotation about its axis. Answer in units of kg · m2

Answer 1

1.75 kg.m²

Step-by-step explanation:

moment of inertia (I) = moment of inertia of ring + 6(moment of inertia of the spoke about the axis of rotation)

`I =`
`I_(rim)+6*I_(spoke)(axis of rotation)`

`I =`
`(M_(rim)*((R)/(2))^2 )+ (6*(1)/(3)M_(spoke)((R)/(2))^2 )`

Given that:

diameter wagon wheel = 1

radius =
`(1)/(2)`

mass of the rim = 4 kg

number of spokes = 6

mass of spoke = 1.5 kg

substituting our values into the above equation, we have:

`I =`
`(4*((1)/(2))^2 )+ (6*(1)/(3)1.5((1)/(2))^2 )`

`I =`
`(4* (1)/(4))+(2*1.5*(1)/(4))`

`I =` 1 + 0.75

`I =` 1.75 kg m²

∴ the moment of inertia of the wagon wheel for rotation about its axis = 1.75 kg.m²