Linear Momentum Definition

Linear Momentum Definition

• Linear momentum (p) is defined as the product of an object's mass and velocity
• Generally, 'momentum' refers to linear momentum

Linear Momentum Equation

• The linear momentum equation is p = mv, where p is proportional to both mass and velocity
• Since velocity is a vector, momentum is also a vector

Linear Momentum and Newton's Second Law

• Newton's second law can be stated as F = Δp / Δt, where F is the net force and Δp is the change in momentum
• For constant mass systems, the equation can be rewritten as F = mΔv / Δt, giving the more common form of Newton's second law

The Impulse-Momentum Theorem

• The impulse-momentum theorem states that a force applied to an object for some time causes a change in momentum
• Impulse (J) is defined as the area under the force-time curve
• Impulse is equal to the change in momentum (J = Δp)

Conservation of Linear Momentum

• The total linear momentum of a system is conserved in the absence of external forces
• The total initial momentum of a system is equal to the total final momentum of the system (Pinitial,total = Pfinal,total)

Linear Momentum Examples

Cue Ball Example

• Linear momentum of a cue ball is calculated as p = mv = (0.50 kg)(0.10 m/s) = 0.05 kg m/s
• Impulse is calculated as J = FΔt = (2.00 N)(0.054 s) = 0.108 kg m/s
• Change in velocity is calculated using the impulse-momentum theorem (J = Δp = m(vfinal - vinitial))

Cue Ball Collision Example

• Momentum is conserved in the collision between the cue ball and the 8-ball
• The 8-ball's velocity after the collision is calculated using the conservation of momentum equation
• The 8-ball moves faster after the collision due to its lighter mass

Star Example

• The total momentum of a system (exploding star) is conserved
• The initial momentum of the star is zero, and the final momentum of the system after the explosion is also zero
• The conservation of momentum principle is used to calculate the trajectories of exploding stars, solar systems, galaxies, and even black holes

Linear Momentum Definition

• Linear momentum (p) is defined as the product of an object's mass and velocity
• Generally, 'momentum' refers to linear momentum

Linear Momentum Equation

• The linear momentum equation is p = mv, where p is proportional to both mass and velocity
• Since velocity is a vector, momentum is also a vector

Linear Momentum and Newton's Second Law

• Newton's second law can be stated as F = Δp / Δt, where F is the net force and Δp is the change in momentum
• For constant mass systems, the equation can be rewritten as F = mΔv / Δt, giving the more common form of Newton's second law

The Impulse-Momentum Theorem

• The impulse-momentum theorem states that a force applied to an object for some time causes a change in momentum
• Impulse (J) is defined as the area under the force-time curve
• Impulse is equal to the change in momentum (J = Δp)

Conservation of Linear Momentum

• The total linear momentum of a system is conserved in the absence of external forces
• The total initial momentum of a system is equal to the total final momentum of the system (Pinitial,total = Pfinal,total)

Linear Momentum Examples

Cue Ball Example

• Linear momentum of a cue ball is calculated as p = mv = (0.50 kg)(0.10 m/s) = 0.05 kg m/s
• Impulse is calculated as J = FΔt = (2.00 N)(0.054 s) = 0.108 kg m/s
• Change in velocity is calculated using the impulse-momentum theorem (J = Δp = m(vfinal - vinitial))

Cue Ball Collision Example

• Momentum is conserved in the collision between the cue ball and the 8-ball
• The 8-ball's velocity after the collision is calculated using the conservation of momentum equation
• The 8-ball moves faster after the collision due to its lighter mass

Star Example

• The total momentum of a system (exploding star) is conserved
• The initial momentum of the star is zero, and the final momentum of the system after the explosion is also zero
• The conservation of momentum principle is used to calculate the trajectories of exploding stars, solar systems, galaxies, and even black holes