How does tension change in a pendulum performing circular motion?

Tension in a pendulum performing circular motion changes due to the combined effects of gravity and centripetal force.

In a pendulum performing circular motion, the tension in the string or rod changes as the pendulum swings back and forth. This is due to the combined effects of gravity, which pulls the pendulum bob downwards, and the centripetal force, which pulls the bob towards the centre of the circle it is moving in. Understanding the role of centripetal force is crucial in analysing circular motion in pendulums.

At the highest point of the swing, the tension is at its maximum. This is because the pendulum bob is momentarily at rest, so the tension in the string must balance the weight of the bob. The tension is equal to the weight of the bob plus the centripetal force required to keep the bob moving in a circle. The concept of acceleration in physics helps explain these changes in tension and motion.

As the pendulum swings down and gains speed, the tension in the string decreases. This is because the bob is moving faster, so the centripetal force is greater. However, the bob is also moving closer to the vertical, so the component of the weight acting along the string and contributing to the tension is decreasing. The net effect is that the tension decreases. This movement showcases the applications of circular motion in pendulums.

At the bottom of the swing, the tension is again at a maximum. This is because the bob is moving at its fastest, so the centripetal force is at its greatest. The bob is also directly below the pivot, so the entire weight of the bob is acting along the string and contributing to the tension. The tension is equal to the weight of the bob plus the centripetal force required to keep the bob moving in a circle.

As the pendulum swings up again, the tension decreases for the same reasons as before. The bob is slowing down, so the centripetal force is decreasing, but the bob is also moving further from the vertical, so the component of the weight acting along the string and contributing to the tension is increasing. The net effect is that the tension decreases. This process involves various types of energy transformation, including kinetic and potential energy.

IB Physics Tutor Summary: In a pendulum's circular motion, tension changes due to gravity and centripetal force. At the top and bottom of the swing, tension is highest because it must counter the bob's weight and provide centripetal force. Mid-swing, tension drops as the bob speeds up, reducing the weight's effect along the string. Essentially, tension varies to balance gravity and maintain circular motion.