AP Physics C: Mechanics / Unit 2: Force and Translational Dynamics
2.1 Properties and Interactions of a System
Notes
A system is the object(s) you choose to analyze. Its center of mass moves as if all external forces act there.
$$x_{cm}=\frac{\sum m_ix_i}{\sum m_i}$$
Practice
2 kg at $x=0$ and 6 kg at $x=4$ m. $x_{cm}=$
$\displaystyle \frac{0+24}{8}$.
Internal forces in a system:
Only external forces matter.
The center of mass is always closer to:
Weighted average.
For a continuous object, the center of mass is:
Continuous version of the weighted average.
A rod of length $L$ has density $\lambda=kx$. Its center of mass is at:
$\displaystyle \frac{\int_0^L kx^2dx}{\int_0^L kx\,dx}=\frac{L^3/3}{L^2/2}$.
Ready for more? Take the Unit 2 test.