Why the velocity of a pendulum bob is maximum at its bottom position?
The velocity of a pendulum bob is maximum at its bottom position because it experiences the maximum acceleration there. This can be explained using the concept of energy conservation and the equations of motion.
To understand why the velocity is maximum at the bottom position, we need to consider the forces acting on the pendulum bob. The two main forces are gravity, which acts downward, and tension in the string or rod, which acts toward the center of motion.
At the highest point of the swing, the pendulum bob is momentarily at rest because the tension in the string or rod cancels out the force of gravity, resulting in zero net force. As the bob begins to swing downward, the tension force remains directed toward the center of motion, while gravity acts downward. This creates a net force that accelerates the bob in the downward direction, causing it to gain speed as it descends.
According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Since the force of gravity remains constant, the only variable affecting the acceleration is the position of the pendulum bob.
As the bob descends, the tension force remains constant, but its direction changes, becoming inclined upward from the vertical. This upward component of tension starts to oppose the downward force of gravity and reduces the net force acting on the bob. As the bob reaches its lowest position, the upward component of tension becomes equal to the force of gravity, resulting in zero net force again.
At this point, the bob has the maximum acceleration because tension is canceling out gravity. Due to the acceleration, the bob gradually increases its velocity as it moves upward on the other side of the swing. As it reaches the highest point again, the process repeats.
In summary, the velocity of a pendulum bob is maximum at its bottom position because it experiences the maximum acceleration there, caused by the difference between the tension force and the force of gravity.