Question

A massless rod of length 1.00 m has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other (See Fig. 1). The system rotates about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached. The kinetic energy of the system is 100 J. What is the angular speed of this system? and what is the moment of inertia?

Answer 1

here,

m1 = 2 kg

m2 = 3 kg

length of rod , l = 1 m

r = 30 cm = 0.3 m

the moment of inertia of the system about the rotation axis , I = m1 * (l - r)^2 + m2 * r^2

I = 2 * ( 1 - 0.3)^2 + 3 * 0.3^2 kg.m^2

I = 1.25 kg.m^2

let the angular speed of the system be w

as the kinetic energy , KE = 0.5 * I * w^2

100 = 0.5 * 1.25 * w^2

solving for w

w = 12.6 rad/s

the angular speed of the system is 12.6 rad/s

the moment of inertia of the system about the rotation axis is 1.25 kg.m^2