06 Circular Motion 🎡
Quantities
Velocity
Angular Displacement
Centripetal Force
θ=sr
\(\theta\) is in radians
Angular Velocity
\(\omega=\frac{\theta}{t}\)
Tangential Velocity
\(v=\frac{s}{t}\)
\(v=\frac{r\theta}{t}\)
\(v=r\omega\)
On Earth 🌏
Outside Earth 🌠
Roller Coaster 🎢
String
*Normal force
*Tensional Force
At the TOP
At the TOP
\(F_c=N+W\)
At the BOTTOM
\(F_c=N-W\)
\(v_{tmin}\)
Occurs when \(N=0\)
\(F_c>W\)
\(\frac{mv^2}{r}>mg\)
\(v_{min}>\sqrt{gr}\)
\(v_{bmin}\)
\(KE_b \rightarrow GPE + KE_t\)
\(\frac{1}{2}mv^2=mg2r+\frac{1}{2}mv_{tmin}^2\)
\(v^2=4gr+gr\)
\(v=\sqrt{5gr}\)
\(F_c=T+W\)
At the BOTTOM
\(v_{tmin}\)
Occurs when \(T=0\)
\(F_c=T-W\)
Orbital Velocity
\(F_c=F_g\)
\(\frac{mv^2}{r}=\frac{GMm}{r^2}\)
\(v=\sqrt{\frac{GM}{r}}\)
R.I. (radially inward)
Questions
Nov 15 Q2
Nov 17 Q2a, b
\(F_c=W\)
\(\frac{mv^2}{r}=mg\)
\(v_{min}=\sqrt{gr}\)
\(v_{bmin}\)
\(KE_{bot}=KE_{top}+GPE\)
\(\frac{1}{2}mv^2=mg(2r)+\frac{1}{2}mgr\)
\(v^2=4gr+gr\)
\(v=\sqrt{5gr}\)