- #1
opus
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- Homework Statement
- Part (d):
Use parts (a), (b), and (c) to argue that $$\vec{N}(t) = \frac{\vec{a}_{v\perp}}{|\vec{a}_{v\perp}|}$$
- Relevant Equations
- $$\frac{d}{dt}(\vec{v}\cdot\vec{v}) = 2\vec{a} \cdot \vec{v}$$
$$\frac{d}{dt}v(t) = \frac{\vec{v}\cdot\vec{a}}{v(t)}$$
$$v(t)\vec{T'}(t) = \vec{a}(t) - \frac{v'(t)\vec{v'}(t)}{v(t)}$$
I need to prove this using the given equations.
$$\vec{N}(t) = \frac{\vec{a}_{v\perp}}{|\vec{a}_{v\perp}|}$$
Here is the entirety of my work up to this point. So far I've wanted to use what I have to find something that is perpendicular to the velocity vector and maybe show that with the dot product but no luck so far and I'm pretty stuck. Any hints to get me started?
$$\vec{N}(t) = \frac{\vec{a}_{v\perp}}{|\vec{a}_{v\perp}|}$$
Here is the entirety of my work up to this point. So far I've wanted to use what I have to find something that is perpendicular to the velocity vector and maybe show that with the dot product but no luck so far and I'm pretty stuck. Any hints to get me started?