The whole situation is equivalent to that of a top precessing about an axis passing through its center of mass.
The relation for the torque in the latter case is given by:
.
We have where is the force acting on the body and is the distance from the origin to the point at which the force is applied.
The force is the tension in the stick T and r is the radius of the circle which the top part of the stick makes as it rotates about the z-axis.
Now .
Also .
Equating the two expressions we have i.e. or . eq 1)
Now we know that the radial component of the tension in the stick provides the necessary centripetal force responsible for its rotational motion i.e since .
Therefore we have .
Substituting this expression for T in eq 1) we obtain:
.
Consider the simplest rigid body, consisting of two point objects each of mass m, connected by...
Consider the simplest rigid body, consisting of two point objects each of mass m, connected by a massless stick of length 2f. Suppose that the motion of this baton is to spin about an axis we'll choose to call , i.e. w = w2. We choose our origin at the center of mass, which is stationary. The angle between the AB axis and i is B. 2. Taking d, what is the external torque on the baton system?
Consider the simplest rigid body, consisting of two point objects each of mass m, connected by a massless stick of length 2f. Suppose that the motion of this baton is to spin about an axis we'll choose to call , i.e. w = w2. We choose our origin at the center of mass, which is stationary. The angle between the AB axis and i is B. 5. What are the moments of inertia in the directions el, ег and ез?
Consider the simplest rigid body, consisting of two point objects each of mass m, connected by a massless stick of length 2f. Suppose that the motion of this baton is to spin about an axis we'll choose to call , i.e. w = w2. We choose our origin at the center of mass, which is stationary. The angle between the AB axis and i is B. 6. Express in the êk basis. Likewise, express the system's angular momentum L, and...
Consider the simplest rigid body, consisting of two point objects each of mass m, connected by a massless stick of length 2f. Suppose that the motion of this baton is to spin about an axis we'll choose to call , i.e. w = w2. We choose our origin at the center of mass, which is stationary. The angle between the AB axis and i is B. 3. Suppose this external torque comes from two strings, applying forces -Tt at A...
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M,sphR2). Let the vertex of the cone be the origin ofthe body frame. By symmetry, choose basis vectors e for the body frame such that the inertia tensor I, is diagonal. Will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? Calculate the inertia tensor in this basis How will the inertia...