Question

3. (25 pts.) An object consists of two uniforin thin rods of mass 6.0 kg and Um, connected by a massless hinge and bent into an 'L'-shape. It can ound one of its ends, with the other rod pointing upward. a. What is ment of mertia of this object? b. How much work is needed to get it to rotate at 4.0 rad/s? c. Suppose it is rotating at 4.0 rad/s, and the ect is straight (and aproximate it to be uniform). What is the falls, so the object is straight (and aproximate final angular velocity?

Answer 1

here,

the mass of each rod , m = 6 kg

the length of rod , l = 1 m

a)

the moment of inertia of this object , I0 = (m * l^2 /3) + m * l^2

I0 = 6 * 1^2 * (1/3 + 1) kg.m^2

I0 = 8 kg.m^2

b)

w0 = 4 rad/s

using Work-energy theorm

work done needed , W = change in kinetic energy

W = 0.5 * I0 * w0^2

W = 0.5 * 8 * 4^2 J = 64 J

c)

let the final angular velocity be w

using conservation of angular momentum

I0 * w0 = I * w

(m * l^2 /3 + m * l^2) * w0 = ( m * (2l)^2 /3) * w

(4/3 * m * l^2) * w0 = (4/3 * (2 m) * (l)^2) * w

w = w0 /2 = 2 rad/s

the final angular velocity will be 2 rad/s