Splung.com Physics Forum

abhishek_das · Joined: 24 Jan 2011 Posts: 1 Location: none

Hi.....

Q.
A cubical block of side 'a' is moving with velocity v on a horizontal smooth plane......
It hits a ridge on its way ahead.....
No odr info given....

Find angular speed of block after it hits the ridge.[/img]

hepcj · Site Admin Joined: 23 Jun 2007 Posts: 121

In this situation, you need to consider the centre of rotation of the cube. If the cube is of side a and the cube hits the ridge at a corner then this will cause it to turn around the centre of the cubic face.
Assuming that the cube doesn't lose any energy in turning (which it would in reality because the cube will have a moment of inertia and some of the energy would go into rotational energy) and carries on moving in the same direction at the same velocity we would just need to calculate the angular velocity, omega.

As we know v = r * omega.
Therefore,
omega = v/r and r is the distance from the corner to the centre of a face it is rotating about.

r = sqrt(a^2 + a^2) = sqrt(2) a

So it will turn at v/(sqrt(2) a)