diff --git a/content/physics/Forces.md b/content/physics/Forces.md index aef1158..95bd5db 100644 --- a/content/physics/Forces.md +++ b/content/physics/Forces.md @@ -260,6 +260,38 @@ It's important to note that the acceleration and velocity vectors at an instant > $v=\frac{2\pi r}{T}$. \ > Since the ball makes 2 revolutions in a second, the period $T$ must be $\tfrac{1}{2}$. $v=\frac{2\pi(0.6\mathrm{m})}{0.5}=7.54$, the unit of that output being meters/second. Substituting that value for the speed $v$ in the acceleration formula, acceleration is $94.7 \mathrm{m}/\mathrm{s}^2$ +## Angular velocity and momentum + +Angular velocity is denoted $\omega$ and is a pseudo-vector usually written in the polar form: $\langle m; \theta \rangle$. From a birds-eye view: +$$ +\omega = \frac{\Delta\theta}{\Delta t} +$$ + +### Uniform Circular Motion +Going off of the equation above for velocity, the angular velocity is simply: +$$ +\omega = \frac{2\pi}{T} +$$ + +### Non-uniform circular motion + +Probably will never need to use this until HL year or the momentum unit (very next one). + +$$ +\omega(t)=\frac{\mathrm{d}\theta}{\mathrm{d}t} +$$ +Angular acceleration: +$$ +\alpha=\frac{\mathrm{d}\omega}{\mathrm{d}t} +$$ + +### Centrifugal force + +Following those formulas (read more [here](https://en.wikipedia.org/wiki/Centrifugal_force)): +$$ +||\vec{F}_C||=m\omega^2r +$$ + # Momentum > [!NOTE]+