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Degree: Theoretical Physics and Applied Maths (Masters) - St. Andrews University
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A pendulum bob will move fastest when the mass is at its lowest point (when x=0). The reason for this is that in the pendulum system energy is transferred between kinetic and gravitational potential energy, and total energy will always be fixed in the system. Gravitational potential energy will be at its minimum when the bob is at the lowest point, meaning that kinetic energy will be at its maximum, resuting in the bob moving fastest at this point.see more
The centripetal force can be thought of as the force that causes circular motion.
When an object moves in a circle a force must always act on it, even when it moves at a constant speed. This is because velocity is a vector (and therefore has both a magnitude and a direction) and the direction the object is moving in is constantly changing.
This constant direction change is an acceleration, and we know from Newton's Second Law that any acceleration must have an force associated with it.
Similarly, the centripetal force must point towards the centre of the circle, and therefore perpendicular to the tangential velocity, to maintain the motion in the circle. If it did not exist the object would 'shoot off' in a direction tangential to the circle.see more