AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Momentum: Principle applied quantitatively to problems in one dimension.
In one dimension, all velocities lie along a single straight line, so momentum conservation becomes a scalar equation once a positive direction is chosen.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 6
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In one dimension, all velocities lie along a single straight line, so momentum conservation becomes a scalar equation once a positive direction is chosen. For two bodies, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where u denotes initial velocity and v final velocity. Velocities opposite to the chosen positive direction are negative. This applies to collisions where bodies separate, to coalescence where they move together with a common final velocity, and to explosions where initial total momentum may be zero.
For example: A 2.0 kg ball moving at 3.0 m s⁻¹ to the right strikes a stationary 1.0 kg ball; if they stick together, the common velocity is found from 2.0 × 3.0 = (2.0 + 1.0)v, giving v = 2.0 m s⁻¹ to the right.
What earns the marks
- Choose and state a positive direction, then write each velocity with the correct sign.
- Write the conservation equation as the sum of initial momenta equals the sum of final momenta.
- Substitute masses and velocities with consistent units, converting grams to kilograms where necessary.
- Solve the resulting linear equation for the unknown velocity, mass or momentum.
- Interpret the sign of the answer to state the direction of motion.
- For coalescence, use a common final velocity for the combined mass.
Common mistakes and how to put them right
Omitting signs for velocities in the opposite direction.
Put it right: Subtract the momentum of objects moving against the chosen positive direction.
Mixing units by substituting grams with kilograms.
Put it right: Convert all masses to kilograms before calculating.
Forgetting that a stationary object has zero initial momentum.
Put it right: Include its term as zero explicitly in the equation.
Exam tips
- Draw a before-and-after diagram with arrows and labels to keep track of directions.
- Write the full conservation equation before rearranging, so method marks are visible.
- Substitute numerical values only after the algebraic equation is formed, reducing arithmetic slips.
Try the lesson
The start of the Momentum: Principle applied quantitatively to problems in one dimension. lesson, made from checked teaching notes for this specification point.
Have a go first
A 1500 kg car moving at 6.0 m/s collides with a 1000 kg car moving in the same direction at 2.0 m/s. They lock together. Calculate their common velocity after the collision.
Listen
In one dimension, all velocities lie along a single straight line, so momentum conservation becomes a scalar equation once a positive direction is chosen. For two bodies, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where u denotes initial velocity and v final velocity. Velocities opposite to the chosen positive direction are negative. This applies to collisions where bodies separate, to coalescence where they move together with a common final velocity, and to explosions where initial total momentum may be zero. For example, a 2.0 kg ball moving at 3.0 m s⁻¹ to the right strikes a stationary 1.0 kg ball; if they stick together, the common velocity is found from 2.0 × 3.0 = (2.0 + 1.0)v, giving v = 2.0 m s⁻¹ to the right. A strong answer earns marks for these points. Choose and state a positive direction, then write each velocity with the correct sign. Write the conservation equation as the sum of initial momenta equals the sum of final momenta. Substitute masses and velocities with consistent units, converting grams to kilograms where necessary. Solve the resulting linear equation for the unknown velocity, mass or momentum. A common slip: Omitting signs for velocities in the opposite direction. Instead, subtract the momentum of objects moving against the chosen positive direction. Exam tip: Draw a before-and-after diagram with arrows and labels to keep track of directions.
Key words
Say what each word means before you turn the card.
One-dimensional vector resolution
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Algebraic modelling of collisions
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Coalescence and explosions
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Consistency of units and signs
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See every definition
- One-dimensional vector resolution
- All velocities lie along a single straight line, so momentum conservation becomes a scalar equation once a positive direction is chosen.
- Algebraic modelling of collisions
- The conservation equation is written as the sum of initial momenta equals the sum of final momenta, then solved as a linear equation.
- Coalescence and explosions
- Bodies may separate in collisions, move together with a common final velocity in coalescence, or have initial total momentum of zero in explosions.
- Consistency of units and signs
- Velocities opposite to the chosen positive direction are negative, and masses and velocities are substituted with consistent units.
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