Answer to Question #250833 in Classical Mechanics for AR Ahmed

Question

Find the number of degree of freedom and set of generalized coordinate of the following

1) rigid body

2) cylinder rolling down on the inclined plane

3) disk vertically rolling on the plane

4) a particle moving along the curve

Answer 1

1. Rigid body has 6 degrees of motion (3 rotational and 3 translational).
2. Being a rigid body, the cylinder has 6 degrees of freedom, but if we consider a descending cylinder rolling without slip, it has 1 rotational degree of freedom. With slip, it has 2 DoF.
3. The disk has 1 rotational degree of freedom on a flat plane because its position can be found only from the radius of the disk and angular speed.
4. The particle moving along a 3D-curve has 3 degrees of freedom.