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Why is the acceleration of a pendulum non-zero at its lowest point?

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There are two forces acting over the pendulum: the force due to gravity (weight), which always points downwards, and the tension of the rope, which is radial to the motion.

Tension is non-zero at the lowest point of the pendulum. Newton's second law states that a change in momentum (and by extension velocity) is caused by a force. The velocity of the oscillating body is changing as it passes through its lowest point: while the modulus remains constant, the direction of velocity is being changed upward. A force must be responsible for this change of velocity. The tension of the rope "pulls" the mass upward so that it follows with its motion.

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    $\begingroup$ Exactly. I just want to add this to the explanation: if $\vec{a}$ were 0, then the rod wouldn't keep moving as a pendulum, but as an straight line, because any movement without acceleration is in straight line. If it is not a straight line it's because of that centripetal aceleration. $\endgroup$ – FGSUZ Feb 21 at 21:57

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