How Fast Does the Tip and Center of Mass of a Falling Rod Travel?

[sweetpete28]

A long, thin rod of mass 9.65 kg and length 10.18 cm is standing stright up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over.

What is the speed of the tip of the rod as it hits table?

What is speed of center of mass of rod?

1/2 m g L = 1/2 x 1/3 m L^2 ω^2


ω= 17 rad/sec

linear velocity = ω L =17 rad/s x 0.102m = 1.73m/s (tip of rod)

For speed of center of mass should I just multiply ω by L/2 (.0509m)...? Yes...right? I get .865 m/s which is half the linear velocity at tip...is linear velocity for center of mass always half of velocity at tip for situation like this?

 

[cepheid]

I haven't checked your math, but recall that v =ωr. Since ω is the same for all points on the rod, it follows that v scales linearly with distance from the centre of rotation.