DennisFetters
Super Member
You should find this educational;
https://www.berkeleyscience.com/airplane.htm
Heres a snip;
The Motion of a Rigid Object
Think of a baseball thrown by a pitcher: as it travels toward the catcher, the ball 'as a whole' is moving in a more or less straight line, but, the ball is also spinning, so that at any instant each point in the ball is travelling at a different speed and a different direction than all the others! Fortunately, it is possible to decompose the motion of a rigid body into two parts, the motion of one point, the center of mass, and the rotation of the object about its center of mass. Thus, we can accurately describe the motion of the ball by specifying at each instant the location of the center of mass and the rotation of the ball about its center of mass.
To specify a rotation in 3-dimensional space it is necessary to specify an axis of rotation as well as the amount of rotation. The axis of rotation can change from moment to moment, and it is a tricky business to keep track of it. However, if we restrict the motion of our airplane to two dimensions, x (forward/backward) and y (up/down), then the axis of rotation will be fixed (the z axis), and we can specify the motion of the plane by specifying the motion of the center of mass and the rotation about the center of mass expressed as an angle.
If a force acts on a rigid body, and the direction of the force is along the line throught the point of application thru the object's center of mass, then it will cause the object to accelerate according to Newton's Second Law of Motion, and that's it. However, if the force is not directed through the center of mass it will also cause the object to rotate. Suppose the center of mass of the object shown to the left is at point p, and a force f is applied to the object. This force will cause the entire object, including point p, to accelerate according to Newton's Second Law of Motion. The force f also produces a torque at point p and an angular acceleration about p according to Newton's Second Law for rotation, which is
a'' = T / I
where a'' is angular acceleration, I is the object's moment of inertia about its center of mass, and T is the applied torque. If there are no other forces acting on the object it will tumble, as shown below.
An object's moment of inertial depends on how the object's mass is distributed about the center of mass. We will assume that the plane's center of mass is located 1/3 of the way back from the nose, and that the plane's moment of inertia about this point is given by 1/20 * m*L2 where m is the mass of the airplane and L is the plane's length (for a discussion of moments of inertia see Common Moments of Inertia)
https://www.berkeleyscience.com/airplane.htm
Heres a snip;
The Motion of a Rigid Object
Think of a baseball thrown by a pitcher: as it travels toward the catcher, the ball 'as a whole' is moving in a more or less straight line, but, the ball is also spinning, so that at any instant each point in the ball is travelling at a different speed and a different direction than all the others! Fortunately, it is possible to decompose the motion of a rigid body into two parts, the motion of one point, the center of mass, and the rotation of the object about its center of mass. Thus, we can accurately describe the motion of the ball by specifying at each instant the location of the center of mass and the rotation of the ball about its center of mass.
To specify a rotation in 3-dimensional space it is necessary to specify an axis of rotation as well as the amount of rotation. The axis of rotation can change from moment to moment, and it is a tricky business to keep track of it. However, if we restrict the motion of our airplane to two dimensions, x (forward/backward) and y (up/down), then the axis of rotation will be fixed (the z axis), and we can specify the motion of the plane by specifying the motion of the center of mass and the rotation about the center of mass expressed as an angle.
If a force acts on a rigid body, and the direction of the force is along the line throught the point of application thru the object's center of mass, then it will cause the object to accelerate according to Newton's Second Law of Motion, and that's it. However, if the force is not directed through the center of mass it will also cause the object to rotate. Suppose the center of mass of the object shown to the left is at point p, and a force f is applied to the object. This force will cause the entire object, including point p, to accelerate according to Newton's Second Law of Motion. The force f also produces a torque at point p and an angular acceleration about p according to Newton's Second Law for rotation, which is
a'' = T / I
where a'' is angular acceleration, I is the object's moment of inertia about its center of mass, and T is the applied torque. If there are no other forces acting on the object it will tumble, as shown below.
An object's moment of inertial depends on how the object's mass is distributed about the center of mass. We will assume that the plane's center of mass is located 1/3 of the way back from the nose, and that the plane's moment of inertia about this point is given by 1/20 * m*L2 where m is the mass of the airplane and L is the plane's length (for a discussion of moments of inertia see Common Moments of Inertia)