Question

A solid cylinder of mass 2() kg rotates about its axis with angular speed 100 rad s⁻¹. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Answer 1

Answer:

Explanation:

Given,

* mass of the solid cylinder = M = 2 kg

* angular speed of the cylinder = w = 100 rad/s.

* radius of the cylinder = R = 0.25 m.

* moment of inertia of a solid cylinder = $\dfrac{4}{3}MR^2$

part (a)

Kinetic energy associated by the rotating cylinder

$K.E.\ = \dfrac{1}{2}Iw^2\\\Rightarrow K.E.\ =\ \dfrac{1}{2}\times \dfrac{4}{3}MR^2\times w^2\\\Rightarrow K.E.\ =\ \dfrac{2}{3}\times MR^2\times w^2\\\Rightarrow K.E.\ =\ \dfrac{2}{3}\times 2\times 0.25^2\times 100^2\\\Rightarrow K.E.\ =\ 833.33\ J$

part (b)

Angular momentum =$Iw\ =\ \dfrac{4}{3}MR^2w\ =\ \dfrac{4\times 2\times 0.25^2\times 100}{3}\ =\ 16.66\ kgm^2s^{-1}$