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A rod standing on frictionless table(Rotation)
A rod of length l is standing on a friction less surface.
A slight impulse is given to the rod and hence the rod starts falling. Find the torque,angular acceleration ,angular velocity, the normal force by the ground and the distance through which the end part of the rod slides on the ground when the rod makes an angle of [tex]\theta[/tex] withe the vertical
Law of conservation of energy and equations of moment of forces.
We can apply the laws of conservation of energy
[tex] mgh = mg\frac{l}{2}(1-cos\theta) + something [/tex]
I don't know what this something would be. It may be the sum of the rotational energy and something. It can't just be rotational energy cause the rod is also sliding on the surface.
From this we would get angular velocity. Differentiating it would give us angular acceleration. Now we can apply the equation of moments. Let x be the distance by which the rod slides.
[tex]N\frac{l}{2}cos\theta = I\alpha [/tex]
The above is about the centra of mass.
[tex]Mg\frac{l}2}sin\theta = I_{0}\beta[/tex]
The above is about the point which touches the ground(ie the endpoint)
What we have to do is to find a relation between alpha and beta and the acc which we get from the law of conservation of energy.
Moreover these are just three equations while we have four variables ( alpha, beta, N and x) and we have no equation containing x.
Homework Statement
A rod of length l is standing on a friction less surface.
A slight impulse is given to the rod and hence the rod starts falling. Find the torque,angular acceleration ,angular velocity, the normal force by the ground and the distance through which the end part of the rod slides on the ground when the rod makes an angle of [tex]\theta[/tex] withe the vertical
Homework Equations
Law of conservation of energy and equations of moment of forces.
The Attempt at a Solution
We can apply the laws of conservation of energy
[tex] mgh = mg\frac{l}{2}(1-cos\theta) + something [/tex]
I don't know what this something would be. It may be the sum of the rotational energy and something. It can't just be rotational energy cause the rod is also sliding on the surface.
From this we would get angular velocity. Differentiating it would give us angular acceleration. Now we can apply the equation of moments. Let x be the distance by which the rod slides.
[tex]N\frac{l}{2}cos\theta = I\alpha [/tex]
The above is about the centra of mass.
[tex]Mg\frac{l}2}sin\theta = I_{0}\beta[/tex]
The above is about the point which touches the ground(ie the endpoint)
What we have to do is to find a relation between alpha and beta and the acc which we get from the law of conservation of energy.
Moreover these are just three equations while we have four variables ( alpha, beta, N and x) and we have no equation containing x.
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