The object below is made up of three point masses joined to each other with rigi
ID: 1608559 • Letter: T
Question
The object below is made up of three point masses joined to each other with rigid massless rods. Each mass is 1 kg and each rod is 1 m long. The object lies on a vertical plane and is allowed to rotate about the rotation axis shown which is perpendicular to the vertical plane. The object is released from rest at the position shown when the mass labeled "1"is lined up with the pivot point along a horizontal line. What is the angular velocity of the object when the mass labeled "2" lines up with the pivot point horizontally?Explanation / Answer
The moment of inertia of the system = ml^2 + ml^2 + 0( as they are point mass)
I = 2ml^2 = 2*1*1^2 = 2 kg m^2
The potential energy at intital point will be:
P1 = mgh + 0+0 (Suppose at horizontal level the potential energy is zero.)
h = l sqrt(3)/2 = 1*sqrt(3)/2 = 0.866 m
Hence P1 = 1*9.81*0.866 = 8.495 J.
At the final point, the potential energy = - mgh (the mass of all three objects are same and the height of the second object will be -h this time.)
P2 = - mgh = -8.495 J
Hence change in potential energy = P2-P1 = -2*8.495 = -16.99 J
This change in potential energy will reflect into the kinetic energy of the system.
Kinetic energy = 0.5 I omega^2 = 0.5*2*omega^2
omega^2 = 16.99
omega = sqrt(16.99) = 4.12 rad/s.