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Esoremada
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Homework Statement
http://puu.sh/57VmL.png
A thin rod, 28.5cm long with a mass of 0.97kg, has a ball with diameter 7.81cm and mass 2.15kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top. The apparatus is free to pivot about the bottom end of the rod.
(A) After it falls through 90°, what is its rotational kinetic energy?
(B) What is the angular speed of the rod and ball after it has fallen through an angle of 90°?
Homework Equations
Ek = 0.5*I*ω2
The Attempt at a Solution
I solved part A successfully by finding the center of mass of the ball and rod and then solving for mgh.
(A)
Centre of mass:
d = Σ(m*d) / Σm
= [0.97*0.285/2 + 2.15*(0.285+0.0781/2)] / (0.97 + 2.15)
= 0.26760657m
Ek = Ep
Ek = m*g*h
= (0.97+2.15)*9.8*0.26760657
= 8.1823 J
But then when I try to solve B I get the wrong answer. Here's what I tried..
(B)
Ek = 0.5*I*ω^2
8.1823 = 0.5*m*r2*ω2
8.1823 = 0.5*(0.97+2.15)*0.267606572*ω2
ω = 8.55813 /s
But this is wrong, and I'm not sure why.
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