Understanding Linear Momentum

Linear Momentum Definition

• Linear momentum ((\vec{p})) is the product of an object's mass ((m)) and velocity ((\vec{v})): (\vec{p} = m\vec{v}).
• Momentum is a vector quantity, sharing the same direction as the velocity vector.
• The SI unit for momentum is kg⋅m/s.

Momentum Comparison

• A truck with a mass of 2,250 kg moving at 25 m/s has a momentum of 56,250 kg⋅m/s.
• A car with a mass of 1,250 kg moving at 47 m/s has a momentum of 58,750 kg⋅m/s, thus, the car has more momentum.

Momentum of a System of Particles

• The total linear momentum ((\vec{P})) of a system is the vector sum of each particle's momentum: (\vec{P} = \vec{p}_1 + \vec{p}_2 +...).
• Given a system with total mass (M = \sum_i m_i) and its center of mass moving at velocity (\vec{v}{CM}), the total momentum is: (\vec{P} = M\vec{v}{CM}).

Problem-Solving Strategy for Momentum

• Conceptualize, ensuring a clear understanding of the situation.
• Categorize, isolating the system of interest.
• Analyze by identifying objects, determining velocities, calculating individual momenta, and summing them vectorially to find total momentum.
• Finalize, checking result consistency and realism.

Quick Quiz: Baseball Momentum

• When a baseball's speed changes from 20 m/s to 40 m/s in the opposite direction after being hit, its final momentum is larger than its initial momentum.

Impulse-Momentum Theorem

• The change in momentum ((\Delta \vec{p})) of an object equals the impulse ((\vec{I})) of the net force applied to it: (\Delta \vec{p} = \vec{I}).

Impulse Definition

• Impulse ((\vec{I})) is the integral of force ((\vec{F}(t))) over the time interval ((\Delta t)): (\vec{I} = \int_{t_i}^{t_f} \vec{F}(t) dt).
• Impulse is a vector quantity with the same direction as the average force.
• Impulse is measured in N⋅s.

Impulse Approximation

• The Impulse Approximation simplifies scenarios by focusing on a large force acting for a short time, ignoring other forces during that interval.