Ball in a Bowl: SHM Derivation (Sliding) + Rolling Teaser | JEE/NEET/Class 11 скачать в хорошем качестве

Ball in a Bowl: SHM Derivation (Sliding) + Rolling Teaser | JEE/NEET/Class 11

Ball in a Bowl Oscillation | Derive SHM Time Period T = 2pi√(R/g) for JEE/NEET Physics In this video, we derive the time period of small oscillations when a ball slides inside a smooth spherical bowl. Starting with the restoring torque due to gravity, we show step by step why the motion is simple harmonic and why the time period comes out to be: T = 2pi√(R/g) [00:00:00] "Introduction & Problem Setup: Understanding Ball in a Curved Space" [00:01:00] "Defining Mass & Radius: Key Parameters of the Ball" [00:02:45] "Center of Curvature & Effective Oscillation Radius" [00:04:15] "Sliding vs Rolling Assumption: Simplifying the Problem" [00:05:40] "Forces in Action: Weight and Normal Reaction Analysis" [00:06:47] "Torque Method: Deriving Angular Acceleration for Sliding Ball" [00:08:42] "Small Angle Approximation: Linearizing for SHM" [00:09:58] "Time Period Formula: T = 2π √(r/g) for Sliding Ball" [00:10:50] "Energy Method Approach: Calculating Potential & Kinetic Energy" [00:12:54] "Total Energy Conservation: Deriving SHM Equation from Energy" [00:14:14] "Velocity Relation: v = θ_dot * r in Circular Motion" [00:15:44] "Final Energy Equation: Setting dE/dt = 0 to Find Motion Equation" We also generalize for a ball of mass M and radius a, and then show how in the point-mass limit it reduces to the classic result. At the end, we introduce the rolling without slipping case and explain why the time period changes when the ball rolls instead of slides (full derivation in the next video). This topic is extremely important for JEE Main, JEE Advanced, NEET UG, and Class 11 Physics (Oscillations + Rotational Motion). It also connects to HC Verma and Exemplar problems on angular SHM. #JEE #NEET #Class11Physics #SHM #Oscillations #BallInBowl #SlidingVsRolling #PhysicsDerivation