- #1

SnappySeudonym

- 1

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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(v

_{g1}) + ∑ F

_{x}dt = M(v

_{g2})

M(v

_{g2}- (v

_{g1})) = ∑ F

_{x}dt

(3/2)LM(ω

_{2}- ω

_{1}) = ∑ F

_{x}dt ⇒ (1)

Conservation of angular momentum (+⊃)

I

_{g}ω

_{1}+ ∑ M

_{a}dt = I

_{g}ω

_{2}+mux

I

_{g}= (1/12)M(3L)

^{2}

I

_{g}= (3/4)L

^{2}M

(3/4)L

^{2}Mω

_{1}+ ∑ (F

_{x}dt)x = (3/4)L

^{2}Mω

_{2}+ mux

using (1)

(3/4)L

^{2}Mω

_{1}+((3/2)LM(ω

_{2}- ω

_{1}))x = (3/4)L

^{2}Mω

_{2}+ mux

x((3/2)LM(ω

_{2}- ω

_{1}- mux) = (3/4)L

^{2}M(ω

_{2}- ω

_{1})

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?