Statement-1 : If a rod is thrown up vertically in absence of air drag, it returns back to the ground without any change in it's angular velocity. Statement-2 : In absence of any torque, the angular momentum of system is conserved.

Engineering

Physics

Newtons Second Law of Motion

Angular Momentum and Conservation of Angular Momentum

Free Body Diagram

Question

Statement-1 : If a rod is thrown up vertically in absence of air drag, it returns back to the ground without any change in it's angular velocity.
Statement-2 : In absence of any torque, the angular momentum of system is conserved.

Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is false, statement-2 is true.

Statement-1 is true, statement-2 is false.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

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When a rod is thrown vertically with no air drag, the only force acting is gravity at its center of mass. Since gravity provides no torque about the center of mass ( $τ = 0$ ), angular momentum $L = I ω$ is conserved. With moment of inertia $I$ constant, angular velocity $ω$ remains unchanged. Statement-1 is true and Statement-2 is the correct explanation.

Final Answer: Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.