Angular momentum when launching projectile

In summary, the equations for the resultant inertial velocities of a projectile launched from a rotating and moving space-based platform B, with a fixed impulse applied at a non-CG location, are as follows: VA(t) = VA + F / mA + wB(t) x R, PA(t) = PA + VA(t) t, VB(t) = VB - F / mB, PB(t) = PB + VB(t) t, wB(t) = wB - F x R / IxxB. The launch location can be calculated using PL(t) = PB(t) + R(t), and the projectile location using PA(t). The acceleration equation aA = aB + wBdot x R + w
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Homework Statement


For a space-based platform B launching a projectile A what are the resultant inertial velocities equations and where do the launch location and projectile end up a little after launch? The platform is rotating and moving thru space and the launch mechanism imparts a fixed N*sec impulse to the projectile. The projectile is not located at the platform CG and the impulse does not act thru the platform CG.

Homework Equations


Ignore gravity, drag, and launcher friction
Impulse acts at projectile CG
mB = platform mass (mA for projectile)
PB = platform initial inertial position of CG (PA for projectile)
VB = platform initial inertial velocity of CG (VA for projectile)
wB = platform initial inertial rotation rate about its CG (wA for projectile)
IxxB = platform moment of inertia (IxxA for projectile)
F = applied impulse force to projectile at time zero
dt = time period after launch to calculate the launch and projectile location
R = distance vector from platform CG to launch location (i.e. projectile CG at launch)

The Attempt at a Solution


These are vectors...
Pre-launch:
VA = VB since they are attached
wA = wB since they are attached
R = PA - PB
After launch:
VB(t) = VB - F / mB this is a constant
PB(t) = PB + VB(t) t
wB(t) = wB - F x R / IxxB this is a constant
VA(t) = VA + F / mA + wB(t) x R this is a constant
PA(t) = PA + VA(t) t
R(t) = R rotated (wB(t) t)

Launch location: PL(t) = PB(t) + R(t)
Projectile location: PA(t)

4. Should I be including more of the parts shown in https://www.physicsforums.com/showthread.php?t=77434
aA = aB + wBdot x R + w x (w x R) + 2 w x VRel + aRel
 
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No, this equation is only appropriate for the acceleration of the projectile relative to the platform. The equations above are appropriate for the velocities and positions.
 

Related to Angular momentum when launching projectile

1. What is angular momentum when launching a projectile?

Angular momentum is a physical quantity that describes the rotational motion of a projectile around its axis of rotation while it is in flight. It is a measure of the amount of rotational motion an object has.

2. How is angular momentum related to the launch of a projectile?

When launching a projectile, the angular momentum is determined by the mass, velocity, and distance from the axis of rotation. The faster the projectile is launched and the farther it is from the axis of rotation, the greater the angular momentum will be.

3. Does angular momentum affect the trajectory of a projectile?

Yes, angular momentum plays a key role in determining the trajectory of a projectile. As the projectile rotates around its axis, it creates a gyroscopic effect that can influence the direction and stability of its flight path.

4. How does the angular momentum change during the flight of a projectile?

The angular momentum of a projectile remains constant throughout its flight, as long as there are no external forces acting on it. This is known as the law of conservation of angular momentum.

5. Can the angular momentum of a projectile be manipulated?

Yes, the angular momentum of a projectile can be manipulated by changing its mass, velocity, or distance from the axis of rotation. This can be done through the use of external forces, such as applying torque or changing the direction of the launch.

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