# Calculating change in angle from an impulse force

• jacobh
In summary, to determine the maximum angle a gun will raise after firing, you need to know the force from the bullet, the weight of the gun, the distance from the center of the barrel to the center of the butt, and the distance from the center of gravity to the center of the butt. You also need to know the perpendicular distance from the line of the barrel to the point of rotation and the velocity of the bullet. Using conservation of angular momentum and energy, you can calculate the initial angular velocity and the maximum angle the gun will raise to. A model for the mass distribution of the barrel and stock is also necessary for calculating the moment of inertia about the pivot point.
jacobh
say there was a rifle that pivoted about the center of its butt..
if you knew the force from the bullet, the weight of the gun and its center of mass, the distance from the center of the barrel to the center of the butt, and the distance from the center of gravity and the center of the butt, how would you go about determining the maximum angle the gun raises after firing?

i'm a little stumped. i don't recall doing any problems like this back in school, so any help would be appreciated :tongue2:

by the way, assume that no other forces acting upon the gun (no hand holding the forearm)

You need to know the perpendicular distance from the line of the barrel to the point of rotation. If you know the velocity of the bullet, you can use conservation of angular momentum to get an initial angular velocity for the barrel. You need a reasonable model for the mass distribution of the barrel and stock to calculate the moment of intertia about the bivot point.

so how can i get the maximum angle from angular velocity?

jacobh said:
so how can i get the maximum angle from angular velocity?
You could use energy conservation for that. If you know the angular velocity imparted to the barrel from angular momentum conservation, the barrel will have rotational kinetic energy about the pivot point. As the CM of the barrel raises, its potential energy increases and the kinetic energy decreases. At the highest point, the kinetic energy is zero and the change in potential energy equals the initial kinetic energy. Calculate the angle from the geometry of the original and final lines of the barrel.

## 1. What is an impulse force?

An impulse force is a large and sudden force applied to an object over a short period of time. It can cause a change in the object's velocity or direction of motion.

## 2. How is an impulse force measured?

An impulse force is typically measured in Newton-seconds (N*s) or pound-seconds (lb*s).

## 3. What is the equation for calculating change in angle from an impulse force?

The equation for calculating change in angle from an impulse force is θ = F*t/I, where θ is the change in angle, F is the impulse force, t is the duration of the force, and I is the moment of inertia of the object.

## 4. How is the moment of inertia of an object determined?

The moment of inertia of an object is determined by its mass and distribution of mass around its axis of rotation. It can be calculated using the equation I = mr^2, where m is the mass and r is the distance from the axis of rotation.

## 5. Can an impulse force cause an object to rotate in the opposite direction?

Yes, an impulse force can cause an object to rotate in the opposite direction depending on the direction and magnitude of the force, as well as the object's moment of inertia and initial angular velocity. This is known as a torque or rotational force.

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