Simple Pendulum Motion Derived Using Torque and the Small Angle Approximation

We use torque = moment of inertia x angular acceleration to derive the equation of motion of a simple pendulum (tau=mL^2 alpha = -mg sin (theta) L , compare the resulting differential equation to that of a mass on a spring (F=ma=-kx), and discuss the so-called small angle approximation, which makes the equations motion nearly identical: a = -(k/m) x for the spring and alpha = - (g/L) theta for the simple pendulum. Note that at 30 degrees (pi / 6 radians), sin (pi/6) differs by less than 5% from pi/6 itself. This derivation is useful for students of AP Physics C Mechanics to know. Under the small angle approximation, the simple pendulum executes simple harmonic motion. #apphysics #apphysicsc #physicslectures #oscillations #simpleharmonicmotion

Видео Simple Pendulum Motion Derived Using Torque and the Small Angle Approximation канала Dr. Pierce's Physics & Math