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SnappySeudonym
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Homework Statement
Given the setup above, what distance x should the ball be away so that there is no impulse reaction at A?
Homework Equations
Conservation of Linear and Angular momentum.
The Attempt at a Solution
Conservation of linear momentum (←+)
(considering the bat alone)
M(vg1) + ∑ Fxdt = M(vg2)
M(vg2 - (vg1)) = ∑ Fxdt
(3/2)LM(ω2 - ω1) = ∑ Fxdt ⇒ (1)
Conservation of angular momentum (+⊃)
Igω1 + ∑ Madt = Igω2 +mux
Ig = (1/12)M(3L)2
Ig = (3/4)L2M
(3/4)L2Mω1 + ∑ (Fxdt)x = (3/4)L2Mω2 + mux
using (1)
(3/4)L2Mω1 +((3/2)LM(ω2 - ω1))x = (3/4)L2Mω2 + mux
x((3/2)LM(ω2 - ω1 - mux) = (3/4)L2M(ω2 - ω1)
x = L/(2(1-mu)
I've seen this problem before, but not with the bat/rod moving at an initial angular speed, can anyone give some insight as to where my solution is wrong, Is it because a used inertia for the COG of the bar and not the end?