All Problems

Dynamics of a solid body

Problem 1.279

A small disc and a thin uniform rod of length \(l\), whose mass is \(\eta\) times greater than the mass of the disc, lie on a smooth horizontal piane. The disc is set in motion, in horizontal direction and perpendicular to the rod, with velocity \(\mathbf{v},\) after which it elastically collides with the end of the rod. Find the velocity of the disc and the angular velocity of the rod after the collision. At what value of \(\eta\) will the velocity of the disc after the collision be equal to zero? reverse its direction?

Reveal Answer
1.279.v′=v(4−η)/(4+η),ω=12v/l(4+η). For η=4 and η>4\begin{aligned} &1.279 . \mathbf{v}^{\prime}=\mathbf{v}(4-\eta) /(4+\eta), \omega=12 v / l(4+\eta) . \text { For } \eta=4\\ &\text { and } \eta>4 \end{aligned}
Prev
Next