Carouselambra - Angular Momentum/Energy, Parallel-Axis A stick figure physics pr
ID: 1380262 • Letter: C
Question
Carouselambra - Angular Momentum/Energy, Parallel-Axis A stick figure physics professor (Mass 13M) is standing in the center of a turn table of mass ((5/6)M) and radius R. He is holding a pole (length 2R), and mass M above hits head. His head (and thus the center of the table) is R/2 away from the end. Initially, they are all rotating at an angular velocity of (omega 2). At some later point, the professor tilts the pole upright so that it is standing straight up and down in the center of the turn table (right next to him, but close enough so that they are both directly over the axis of rotation). What is the moment of inertia of the pole before it is turned upright?Explanation / Answer
Before it is turned upright
Length of pole = J = 2 R
Mass of pole =M
Distance from centre of pole to axis = d = 2R - R/2 = 1.5 R
Moment of inertia of pole about the rotating axis = 1/12 M J2 + M d2
= 1/12 M (2R)^2 + M (1.5R)^2
= 1/3 M R2 + 9/4 MR2
= (31/12) MR2