Why it makes no sense is because centre of mass (COM) is a place where the mass of the whole body is present. Why can't we think like this: "When the semicircular wire is stretched and made to a straight wire the COM will be at the centre, right?". But COM of semicircular wire is $2R/\pi$ from th...

I'm taking an introductory thermodynamics course, and according to my professor, the heat capacity of an ideal gas is $\frac{3}{2}R \approx$ 12.5. Since ideal gases don't have any attraction between molecules, every bit of energy put into the system goes towards increasing the Kinetic energy of m...

Suppose I have some material in solid-state (say), I cut it into two parts. Take the first cut it into two parts, take the first cut it into two parts, and then repeat this again and again. There will be a point when the substance loses its solid property. I'm interested in this point. I realize ...

The equations of motion that describe the above situation is given by: $$ m \ddot{x_1} = -2kx_1 + kx_2 $$ $$ m \ddot{x_2} = -2kx_2 + kx_1 $$ Now I want to work out the potential energy of this system. How would I use the equation: $$ V(x) = - \int F(x) \hspace{.1cm} dx$$ to calculate the potenti...