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Please help me out with this question on toppling.....

 
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abhishek_das



Joined: 24 Jan 2011
Posts: 1
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PostPosted: Wed Jan 26, 2011 5:19 pm    Post subject: Please help me out with this question on toppling..... Reply with quote

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]
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hepcj
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Joined: 23 Jun 2007
Posts: 125

PostPosted: Thu Feb 03, 2011 7:35 pm    Post subject: Reply with quote

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)
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