- #1

brochesspro

- 155

- 22

- TL;DR Summary
- For obtaining the velocity of a rod slipping on a frictionless floor, why should we use the principle of conservation of energy and not the SUVAT equations, and is the normal reaction a conservative force?

The question is:

A uniform rod of length ##L## stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What is the rod's angular velocity when it makes an angle of 30 degrees with the floor, assuming the rod does not slip?

I do know what steps to take to solve this problem, and I got the correct answer: $$\omega = {\left(\frac{24g}{13L}\right)}^{1/2}$$

The method is to apply the law of conservation of energy and use a constraint relation of ##v = \frac{\sqrt 3}4 L\omega##, to obtain the given answer. You can ask me if you need my help getting the constraint relation.

My question is, why are we applying the law of conservation of energy? It is applied when only conservative forces act on a system, right? But here, along with the earth's gravitational force, normal force by the floor is being applied too.

My other question is whether the acceleration of the rod's centre of mass is constant or not, which would mean that the normal force is constant. Thus, if that is so, we can find the angular velocity of the rod using the SUVAT equations.

That is it, I guess. Thank you for going through my question.

A uniform rod of length ##L## stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What is the rod's angular velocity when it makes an angle of 30 degrees with the floor, assuming the rod does not slip?

I do know what steps to take to solve this problem, and I got the correct answer: $$\omega = {\left(\frac{24g}{13L}\right)}^{1/2}$$

The method is to apply the law of conservation of energy and use a constraint relation of ##v = \frac{\sqrt 3}4 L\omega##, to obtain the given answer. You can ask me if you need my help getting the constraint relation.

My question is, why are we applying the law of conservation of energy? It is applied when only conservative forces act on a system, right? But here, along with the earth's gravitational force, normal force by the floor is being applied too.

My other question is whether the acceleration of the rod's centre of mass is constant or not, which would mean that the normal force is constant. Thus, if that is so, we can find the angular velocity of the rod using the SUVAT equations.

That is it, I guess. Thank you for going through my question.