Conservation of Angular momentum problem

[haruspex]

w=sqrt(2gh)/d

use energy conservation, so delta(GPE)=1/2Iw^2?

Right. The final challenges are to calculate I correctly for the rod plus block, and express the ΔGPE as a function of the angle.

 

[i_hate_math]

okay,
now w=sqrt(mgh)/d
mgl=0.5Iw^2, where l is change in height
and by subing in all the mess l=h
and then ø=arccos[(d-h)/d]=36.8

 

[i_hate_math]

okay,
now w=sqrt(mgh)/d
mgl=0.5Iw^2, where l is change in height
and by subing in all the mess l=h
and then ø=arccos[(d-h)/d]=36.8

soz w=sqrt(2gh)/d i meant

 

[kinemath]

l is not equal to h

 

[i_hate_math]

l is not equal to h

I mean after subing in all the values, i got l=h, or did i do the wrong calculations?

 

[kinemath]

is h the original height and l the final height?

 

[kinemath]

How did you get l=h?

 

[i_hate_math]

How did you get l=h?

L=(0.5I*w^2)/mg

 

[kinemath]

Hmm... I don't think energy is conserved as it is an inelastic collision.

 

[i_hate_math]

Hmm... I don't think energy is conserved as it is an inelastic collision.

After the collison, mechanical energy is conserved

 

[haruspex]

now w=sqrt(2gh)/d
mgl=0.5Iw^2, where l is change in height

Right, though we will have to be careful not to confuse l (lower case L,)with I (uppercase I). To avoid confusion I'll write H for the change in height and I_mom for moment of inertia. Also, the m in there should be for the mass of the rod plus block, not just the block, and H is the change in height of the mass centre of that combination. We will return to that later.

As I said, you next need to figure out the right value for I_mom. This is for the rod and block as a combined system. Think carefully.

 

[i_hate_math]

Right, though we will have to be careful not to confuse l (lower case L,)with I (uppercase I). To avoid confusion I'll write H for the change in height and I_mom for moment of inertia. Also, the m in there should be for the mass of the rod plus block, not just the block, and H is the change in height of the mass centre of that combination. We will return to that later.

As I said, you next need to figure out the right value for I_mom. This is for the rod and block as a combined system. Think carefully.

Since the block is treated as a particle, the Imom would be 1/3mw^2 right?

 

[i_hate_math]

Since the block is treated as a particle, the Imom would be 1/3mw^2 right?

(1/3)(m+M)w^2 is what i meant.

 

[Let'sthink]

Let ω be the instantaneous angular velocity of the rod as well as the stuck block about the pivot just after impact.
Te expression for angular momentum of rod + block just after impact {(Md²/3) + (md²)}ω. Equating this with initial angular momentum of the block just before impact gives you ω
To find θ, find the change in potential energy of the rod and the stuck block, when the rod reaches the angle θ and momentarily come to rest. This then is ro be equated with initial rotational KE of the of the block using formula 0.5Iω², where I = {(M/3)+m}d². { Note I(rod) = M(d²/3) and that of stuck small block = md²}

 

[haruspex]

(1/3)(m+M)w^2 is what i meant.

First, you don't mean w², I hope. A moment of inertia is a mass multiplied by the square of a distance.
Secondly, you need to consider each body separately and add up their moments. What did you find for the moment of the block about O in post #26?

 

[haruspex]

Let ω be the instantaneous angular velocity of the rod as well as the stuck block about the pivot just after impact.
Te expression for angular momentum of rod + block just after impact {(Md²/3) + (md²)}ω. Equating this with initial angular momentum of the block just before impact gives you ω
To find θ, find the change in potential energy of the rod and the stuck block, when the rod reaches the angle θ and momentarily come to rest. This then is ro be equated with initial rotational KE of the of the block using formula 0.5Iω², where I = {(M/3)+m}d²

Please do not spoon-feed @i_hate_math. He/she needs to get the hang of figuring these things out.

 

[i_hate_math]

First, you don't mean w², I hope. A moment of inertia is a mass multiplied by the square of a distance.
Secondly, you need to consider each body separately and add up their moments. What did you find for the moment of the block about O in post #26?

Yeah i didnt. I think i know where i went wrong. Its MoI again, nasty little bugger, the MoI of a point is simply md^2, and i forgot to add this into my calculation.