Recent content by physicsdude101

I think I worked it out: Do the principal axes point in the directions (-2,3,3),(3,1,1),(0,1,-1)?

I don't get it from the drawing I made either. Oops should've said I did one earlier.

Homework Statement Three equal point masses, mass M, are located at (a,0,0), (0, a, 2a) and (0, 2a, a). Find the centre of mass for this system. Use symmetry to determine the principle axes of the system and hence find the inertia tensor through the centre of mass. (based on Hand and Finch...

Well the equations also imply (not derived directly here) that as time goes on, the tension in the string also gets larger and larger. At some point the string will break due to the tension in the rope being too high. Then the mass will initially travel at the velocity is was traveling at an...

The special value of time I notice is $$t=\frac{R\sqrt{R^2-r^2}}{V_0r}$$ since as t approaches this time, the velocity approaches infinity. This corresponds to the mass m moving faster and faster as I pull on the string in order to keep it moving in a circle of constant radius. Of course...

Thanks @kuruman for the better drawn diagram. I have a new solution taking in mind what was said above. Here it is: First from the diagram and using the Pythagoraean Theorem we can immediately deduce that $$\tan\theta=\frac{r}{\sqrt{R^2-r^2}}$$. Upon drawing a FBD with the only force acting...

I think I have a solution. First define the two masses as being h metres off the ground initially. Then by the conservation of energy, $$E_{initial}=E_{final}$$ $$\implies mgh+(2m)gh=\frac{1}{2}mv^2+\frac{1}{2}(2m)v^2+\frac{1}{2}I\omega^2+mg(2h)$$ $$\implies...

I think I'll use Cartesian coordinate system with h as the initial height from the ground in both masses. Then the finish height would be 0 for mass 2m? Although I'm not sure about the final height for the second mass. I suppose another relevant equation would be $$v^2-v_0^2=2a\Delta x$$

r is unknown. I'm not sure about potential energy because I don't know where the ground is defined. I'm also not sure about acceleration. I copied the problem statement exactly as I saw it in my homework problems.

Thank you. I think all my questions have been answered then. :)

Ah I think I get it. So my value of -5mg is correct the way I defined N, and it just means that at φ=π it has magnitude 5mg in the positive y direction? Thus the net force would have a magnitude 5mg-mg=4mg in the positive y direction?

I'm unsure of what you're asking.

Sorry that is what I meant to say. I am supposed to do it with conservation of energy rather than Newton's laws but I am unsure how to do so.

I don't know how to get the acceleration without using Newton's Laws, which is what the question is asking me to do.

Homework Statement Consider a massive pulley of mass m and radius r shown in the figure below, with two objects hanging off it having masses m and 2m, respectively. The pulley can be considered as a uniform disk, and the string is massless, does not stretch and does not slip. By considering...