- #1
JulienB
- 408
- 12
Hi everybody! I'm preparing myself for upcoming exams, and I struggle a little with conservation of angular momentum. Can anybody help me understand how to solve such problems?
1. Homework Statement
(for a better comprehension, see the attached image)
We have a wooden cylinder of mass mZ = 600g and of radius r0 = 5cm, which can rotate around its symmetry axis. Someone shoots on it, and the projectile has the mass mG = 5.0g and initial velocity v = 80m/s. The distance between the linear trajectory of the projectile and the rotation axis of the cylinder is r1 = 3.0cm. The projectile penetrates the cylinder and stays stuck at a distance of r2 = 3.5cm from the rotation axis of the cylinder.
a) What is the frequency of rotation f of the cylinder after the impact? Where and how should you shoot the projectile in order to obtain maximum/minimum frequency?
b) Which part of the kinetic energy is used to deform the wooden cylinder?
c) If the cylinder was not fixed on a rotation axis but on a thread, what would be the differences to previous case when the projectile hits the cylinder?
So I imagine both conservation of linear momentum and of angular momentum are important. We also know that ω = 2πƒ.
Okay I give it a go:
We know that the linear momentum is conserved, that the cylinder is not moving before the collision and that the two objects are moving together after the collision:
mG ⋅ v = (mG + mZ) ⋅ v'
Here I already see a problem: v' is supposed to be the tangential velocity of the system cylinder-projectile after the collision, but I believe a projectile located at r2 = 3.5cm does not have the same tangential velocity as a point located at r0 = 5.0cm. Is that correct? Then we would have mG ⋅ v = mG ⋅ vG' + mZ ⋅ vZ', which is also not so great.
I encounter the same problem with the conservation of angular momentum:
mG ⋅ v ⋅ r0 = (mG + mZ) ⋅ v' ⋅ r0
or
mG ⋅ v ⋅ r0 = mG ⋅ vG' ⋅ r2 + mZ ⋅ vZ' ⋅ r0
?
I feel like I'm missing something, since none of those equations lead me anywhere :( Furthermore, I never manage to involve r1 in the equations, which obviously plays a role because of the 2nd part of the question. Can someone give me a clue so that I clarify my misunderstandings?Thank you very much in advance.Julien.
1. Homework Statement
(for a better comprehension, see the attached image)
We have a wooden cylinder of mass mZ = 600g and of radius r0 = 5cm, which can rotate around its symmetry axis. Someone shoots on it, and the projectile has the mass mG = 5.0g and initial velocity v = 80m/s. The distance between the linear trajectory of the projectile and the rotation axis of the cylinder is r1 = 3.0cm. The projectile penetrates the cylinder and stays stuck at a distance of r2 = 3.5cm from the rotation axis of the cylinder.
a) What is the frequency of rotation f of the cylinder after the impact? Where and how should you shoot the projectile in order to obtain maximum/minimum frequency?
b) Which part of the kinetic energy is used to deform the wooden cylinder?
c) If the cylinder was not fixed on a rotation axis but on a thread, what would be the differences to previous case when the projectile hits the cylinder?
Homework Equations
So I imagine both conservation of linear momentum and of angular momentum are important. We also know that ω = 2πƒ.
The Attempt at a Solution
Okay I give it a go:
We know that the linear momentum is conserved, that the cylinder is not moving before the collision and that the two objects are moving together after the collision:
mG ⋅ v = (mG + mZ) ⋅ v'
Here I already see a problem: v' is supposed to be the tangential velocity of the system cylinder-projectile after the collision, but I believe a projectile located at r2 = 3.5cm does not have the same tangential velocity as a point located at r0 = 5.0cm. Is that correct? Then we would have mG ⋅ v = mG ⋅ vG' + mZ ⋅ vZ', which is also not so great.
I encounter the same problem with the conservation of angular momentum:
mG ⋅ v ⋅ r0 = (mG + mZ) ⋅ v' ⋅ r0
or
mG ⋅ v ⋅ r0 = mG ⋅ vG' ⋅ r2 + mZ ⋅ vZ' ⋅ r0
?
I feel like I'm missing something, since none of those equations lead me anywhere :( Furthermore, I never manage to involve r1 in the equations, which obviously plays a role because of the 2nd part of the question. Can someone give me a clue so that I clarify my misunderstandings?Thank you very much in advance.Julien.