Question

1. sachant que la fréquence avec laquelle tourne un objet est $f = \frac{v}{2\pi r}$, trouvez la relation mathématique qui relie la force centripète à la fréquence de rotation.

Explanation:

Step1: Recall centripetal force formula

The centripetal force is given by $F = \frac{mv^2}{r}$

Step2: Isolate $v$ from frequency formula

Given $f = \frac{v}{2\pi r}$, rearrange to get $v = 2\pi r f$

Step3: Substitute $v$ into force formula

Substitute $v = 2\pi r f$ into $F = \frac{mv^2}{r}$:
$F = \frac{m(2\pi r f)^2}{r}$

Step4: Simplify the expression

Expand and simplify:
$F = \frac{m \cdot 4\pi^2 r^2 f^2}{r} = 4\pi^2 m r f^2$

Answer:

$F = 4\pi^2 m r f^2$