I do a lot of fibrework (carding wool, spinning yarn, weaving, etc.) and I've noticed a funny behaviour that anything long and flexible, which can withstand significant torque exhibits. If I take a piece of yarn and begin to twist it, it remains twisted so long as I keep it in tension (the piece ...

I can find 3 displacement $\vec d_1 ,\vec d_2, \vec d_3$ and use them as basis so that a displacement is $\vec d=a\vec d_1 +b\vec d_2+c \vec d_3$. I can find 3 forces $\vec F_1 ,\vec F_2, \vec F_3$ and use them as basis so that a force is $\vec F=a\vec F_1 +b\vec F_2+c \vec F_3$. So the basis are...

In my physics course, we are doing an experiment rolling disks and spheres down an incline (assuming there is no slipping). In doing the derivations (assuming a moment of inertia of $\frac25mR^2$ for sphere and $\frac12mR^2$ for disk) I have derived that the final velocity should be $\sqrt{\frac{...