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How do you calculate the center-of-mass velocity?

  1. Identify all objects in the system. 2. Determine the mass and velocity of each object. 3. Calculate the sum of the individual momenta (mᵢvᵢ). 4. Calculate the sum of the individual masses (mᵢ). 5. Divide the total momentum by the total mass: v⃗cm=∑p⃗i∑mi=∑(miv⃗i)∑mi\vec{v}_{\mathrm{cm}}=\frac{\sum \vec{p}_{i}}{\sum m_{i}}=\frac{\sum\left(m_{i} \vec{v}_{i}\right)}{\sum m_{i}}

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How do you calculate the center-of-mass velocity?
1. Identify all objects in the system. 2. Determine the mass and velocity of each object. 3. Calculate the sum of the individual momenta (mᵢvᵢ). 4. Calculate the sum of the individual masses (mᵢ). 5. Divide the total momentum by the total mass: $\vec{v}_{\mathrm{cm}}=\frac{\sum \vec{p}_{i}}{\sum m_{i}}=\frac{\sum\left(m_{i} \vec{v}_{i}\right)}{\sum m_{i}}$
How do you apply conservation of momentum to solve collision problems?
1. Define the system. 2. Check for external forces. If net external force is zero, momentum is conserved. 3. Write the conservation of momentum equation: Total momentum before = Total momentum after. 4. Solve for the unknown variable(s).
What steps should you take to quantitatively analyze 1D and 2D collisions?
1. Choose your system carefully. 2. Apply conservation of momentum along each axis (x and y). 3. Account for the vector nature of momentum, using positive and negative signs for directions. 4. Solve the resulting equations for the unknowns.
How do you determine if a collision is elastic or inelastic?
1. Calculate the total kinetic energy before the collision. 2. Calculate the total kinetic energy after the collision. 3. Compare the initial and final kinetic energies. 4. If kinetic energy is conserved (KE_initial = KE_final), the collision is elastic. If kinetic energy is not conserved, the collision is inelastic.
How to calculate impulse?
1. Identify the force acting on the object and the time interval over which it acts. 2. If the force is constant, multiply the force by the time interval: J = FΔt. 3. If the force is not constant, integrate the force with respect to time: J = ∫F dt. 4. Alternatively, calculate the change in momentum: J = Δp = mv_f - mv_i.
Define linear momentum.
A measure of an object's mass in motion, quantifying how much 'oomph' it has.
What is center-of-mass velocity?
The average velocity of a system of objects, treating the system as a single entity.
Define impulse.
The change in momentum of an object when the object is acted upon by a force for an interval of time. Mathematically, it's the integral of force with respect to time, but more simply, it is the product of the average force and the time interval for which it acts.
What is an isolated system in the context of momentum?
A system where no net external force acts, and thus the total momentum remains constant.
Define the Impulse-Momentum Theorem.
The change in a system's total momentum equals the impulse exerted on it from outside the system: $\vec{J}=\Delta \vec{p}$
What is the effect of an external force acting on a system?
The change in momentum of the system will equal the impulse of that force.
What happens when the net external force on a system is zero?
The total momentum of that system stays constant.
What is the effect of impulse on momentum?
Impulse causes a change in momentum.