Answer to Question #249460 in Analytic Geometry for Barbie

Question

Subject : Analytical Dynamics

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

1) Rigid body

2) Cylinder rolling down on inclined plane

3) Disk vertically rolling on a plane

4) A particle moving along a 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.