Differentiate between Simple Pendulum and Compound Pendulum.
ANSWER : The differences between a simple and a compound pendulum are given below. Let's start with the simple pendulum!
Simple Pendulum :
1. A simple pendulum consists of a mass (known as the bob) attached to a string or rod of negligible mass and fixed at a single point.
2. The bob of a simple pendulum swings back and forth in a single plane, like the back-and-forth motion of a swing.
3. The motion of a simple pendulum is periodic, meaning it repeats itself over time.
4. The time it takes for one complete swing of the pendulum, known as the period (T), depends only on the length of the string (l) and the acceleration due to gravity (g).
Formula: \(T = 2\pi\sqrt{\frac lg}\), where T is the period, l is the length of the string, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Compound Pendulum :
1. A compound pendulum, also known as a physical pendulum, consists of a rigid body (like a plank or a metal rod) that can rotate freely about a horizontal axis.
2. Unlike a simple pendulum, the motion of a compound pendulum is not restricted to a single plane. It can rotate in multiple planes due to its rigid body structure.
3. The period of a compound pendulum depends on various factors, including the shape, size, and mass distribution of the rigid body.
4. The formula for the period of a compound pendulum is more complex and depends on the moment of inertia (I) of the body, the distance of the axis of rotation from the center of mass (h), and the gravitational acceleration (g).
Formula: \(T = 2\pi\sqrt{\frac{I}{{mgh}}}\), where T is the period, I is the moment of inertia, m is the mass of the body, g is the acceleration due to gravity, and h is the distance of the axis of rotation from the center of mass.
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