Question

The topmost and bottommost velocities of a disk are `v_2` and `v_2` in the same direction. The radius is R. Find the angular velocity `omega`?

Answer 1

See below.

Explanation:

Concerning the plane motion of a rigid body, the velocity field obeys the Poisson formula

`vec v(p_1) = vec v(p_2) + vec omega xx (p_1-p_2)`

now the distance between the topmost and the bottommost points is `norm(p_1-p_2) = 2R` then

`vec v(p_1) - vec v(p_2) = vec omega xx (p_1-p_2)`

and concluding

`norm(vec omega) = norm(vec v_1-vec v_2)/(2R)`