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:

$KE = \frac{1}{2}Iw^2$

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:

$KE = \frac{1}{2}(\frac{1}{3}mL^2w^2)$

$KE = \frac{1}{6}mL^2w^2$

Plug in the given values:

$KE = \frac{1}{6}(0.63)(0.82^2)(4.2^2) = 1.245 J$