Correct Answer - Option 3 : force and linear momentum
The correct answer is option 3) i.e. force and linear momentum
CONCEPT:
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Angular momentum: The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. It is related to the rotational motion of a rigid body.
- Angular momentum also obeys the law of conservation of momentum i.e. angular momentum before and after is conserved.
- Angular momentum, L = I × ω
Where I is the moment of inertia and ω is the angular velocity.
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Rotational analog of Newton's Second Law: It states that the sum of the torques (Στ) on a rotating system about a fixed axis equals the product of the moment of inertia (I) and the angular acceleration (α). It is given by
\(⇒ Σ τ = I \times α\)
We know that the rate of change of angular velocity = angular acceleration.
- Rate of change of angular momentum,
\(⇒ \frac{dL}{dt} = \frac{d(I\omega)}{dt} = I \times \frac{d\omega}{dt} = I \times α\)
\(\Rightarrow Σ τ = I \times α = \frac{dL}{dt}\)
EXPLANATION:
Torque is the rate of change of angular momentum.
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Speed is the time rate of change of movement of an object, whereas velocity is the time rate of change of movement and direction of an object.
- Acceleration is the rate of change of velocity for a duration of time.
- From Newton's second law, force is the rate of change of linear momentum of an object.
- Energy is the capacity of an object to do work.
- Hence, the correct answer is force and linear momentum.
