Homework Statement
By using chain rule of differentiation, show that:
$$ \frac{\mathrm{d} sin\phi }{\mathrm{d} t} = \dot{\phi} cos\phi , \frac{\mathrm{d} cos\phi }{\mathrm{d} t} = -\dot{\phi} sin\phi , $$
Homework EquationsThe Attempt at a Solution
I got this right for a homework problem...
I'm currently working on the exact same question, and using : $$-\frac{\partial U}{\partial x} = F$$ I integrated ##F=-kx## and got : $$T= \frac{1}{2}m\dot{x}^{2},U = kx^{2}$$
Is this correct?
Is T=(1/2)mv^2 always what you substitute in for a simple kinematics question?
Thank you so much!
My professor emphasized the geometric interpretation of the answers that I completely forgot about those definitions.
Worked like magic, problem solved.
By the way, is there a reason why you're writing ##\vec{i}## and not ##\hat{i}##?
I'm used to ##\hat{i}## as a notation...
Homework Statement
Prove: $$\frac{d\hat{r}}{dt} = \dot{\phi} \hat{\phi }$$ and $$\frac{d\hat{\phi}}{dt} = -\dot{\phi} \hat{r }$$Homework EquationsThe Attempt at a Solution
I solved this for an Analytical Mechanics assignment a month ago, and completely forgot how it goes..
$$\hat{r} ⊥...
Thank you Angry Citizen :)
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Homework Statement
I'm currently working on doing an investigation on the relationship between kinematics and base running techniques in baseball. I'm trying to find out if "rounding the bases" is better than running straight to each base and turning, but I haven't found how I should preform...