Force's Rotational and Translational influences

[Tarnasa]

Problem
How would i find how a force such as a rocket engine would add rotational and translational momentum to an object, supposing i know the distance perpendicular to the direction of the force. I also know the mass of the object, the velocity and spin of the object, and the energy of the force acting upon the object.

My attempt
My first attempt was to use the perpendicular distance: P and multiply it by the force F divided by the mass M. This would give me a very crude rotational amount, however it could easily lead to problems if P was too big and then the rotational force would go beyond the actual amount of energy in the system.

I eventually got to something like this:
Turn = (1 - 1 / P) * 10 * (F / M^1.4)
and
Forward = (F / M) - (P * 2 * pi) * (Turn / 360)

Which approximates it OK
however this still seems to be far off and i would appreciate it if someone could explain a more precise but not necessarily complex way to solve it.

 

[anathema]

Thank you for your question. Calculating the effect of a rocket engine on an object's rotational and translational momentum can be done using basic physics equations and principles. I will break down the steps below:

1. Determine the force acting on the object:
The force acting on the object is the force of the rocket engine. This can be calculated by using the energy of the force and the distance over which it acts. The formula for force is F = ΔE/Δx, where ΔE is the energy of the force and Δx is the distance over which it acts.

2. Calculate the torque:
To determine the rotational effect of the force, we need to calculate the torque, which is the rotational equivalent of force. The formula for torque is T = rF, where r is the distance from the axis of rotation to the point where the force is applied and F is the force acting on the object.

3. Find the moment of inertia:
The moment of inertia is a measure of an object's resistance to rotational motion. It depends on the object's mass, shape, and distribution of mass. You can use the formula I = mr^2, where m is the mass of the object and r is the distance from the axis of rotation to the object's center of mass.

4. Calculate the angular acceleration:
Using Newton's second law of motion, we can calculate the angular acceleration of the object. The formula is α = T/I, where T is the torque calculated in step 2 and I is the moment of inertia calculated in step 3.

5. Determine the change in angular velocity:
To find the change in angular velocity, we use the formula ω = ω0 + αt, where ω0 is the initial angular velocity of the object, α is the angular acceleration calculated in step 4, and t is the time over which the force acts.

6. Calculate the change in translational momentum:
The change in translational momentum can be calculated using the formula Δp = FΔt, where F is the force acting on the object and Δt is the time over which the force acts.

7. Determine the change in velocity:
To find the change in velocity of the object, we use the formula v = v0 + Δp/m, where v0 is the initial velocity of the object, Δp is the change in translational momentum calculated in step 6, and m is the mass