Question

A rod of length 0.82 m, rotating with an angular speed, 4.2 rad/s, about axes that pass perpendicularly through one end, has a mass of 0.63 kg, which is distributed uniformly along its length. Find the kinetic energies of the rod.

Answer 1

Hi there!

`\large\boxed{KE =1.245 J}}`

The equation of angular kinetic energy is:

`KE = (1)/(2)Iw^2`

Where:

I = moment of inertia (kgm²/s)

ω = angular speed (rad/sec)

A rod rotated about one of its endpoints has a standard moment of inertia of 1/3mR², so:

`KE = (1)/(2)((1)/(3)mL^2w^2)`

`KE = (1)/(6)mL^2w^2`

Plug in the given values:

`KE = (1)/(6)(0.63)(0.82^2)(4.2^2) = 1.245 J`