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Kind of a silly question, but imagine there's a pendulum swinging that has some fixed length l and it's at some angle $\theta$, then with respect to us, the forces on the bob are: $$F_{rad} = mg \cos(\theta) - T$$ where $F_{rad}$ is radial component of net force and T is tension in the string, and $$F_{Tan} = mg\sin(\theta)$$ where $F_{Tan}$ is tangential component of the net force on Bob. When the bob is at its lowest point, $\theta = 0$ and so the net force on bob is 0, but isn't there always a net force on bob that causes change in direction of velocity to make sure it doesn't move in a straight line? Or does that force only exist in bob's frame of reference?

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    $\begingroup$ Are you sure that $T=mg$ at the bottom? $\endgroup$ Commented May 15, 2021 at 10:22
  • $\begingroup$ Thanks for replying. I think that is my central problem, we say that T - mg = F_c where F_c is centripetal force but isn't centripetal force just the tension in the string? $\endgroup$ Commented May 15, 2021 at 10:35
  • $\begingroup$ I'm thinking Tension in the string is greater than mg, but I can't say why would that be the case? Isn't tension just the reactive force? $\endgroup$ Commented May 15, 2021 at 10:41
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    $\begingroup$ Replace string with a spring then think about it. I think you should get it. $\endgroup$ Commented May 15, 2021 at 11:31
  • $\begingroup$ I think you're saying the string gets stretched which would make sense but don't we assume that the length of the string is constant? $\endgroup$ Commented May 16, 2021 at 5:44

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No, tension in the string at lowest point can be found from Newton's Second law: $$\mathbf {F_{net}}=m\mathbf a$$ At lowest point, due to circular motion, we will have radial acceleration $\frac {v^2}{r}$. So, we have: $$T-mg=\frac {mv^2}{r}$$ If you know the initial value of $\theta$, you can also find out the value of $T$ in terms of $\theta$ by making use of energy conservation to find $v$ at the lowest point.

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  • $\begingroup$ That makes sense, but what causes this extra centripetal force? Why is tension in the string more than force of gravity? Is the string getting stretched? $\endgroup$ Commented May 16, 2021 at 5:45
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    $\begingroup$ No string is not getting stretched. The centripetal acceleration is present whenever a body undergoes curvilinear motion. It is the acceleration necessary to change the velocity of a point. $\endgroup$ Commented May 16, 2021 at 5:49

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