--- title: "Linear Momentum Speed Review" description: "Learn every thing about linear momentum and impulse. We've simplified to 2 equations! + 10 Questions to help you master momentum." featured_image: "https://nerd-notes.com/wp-content/uploads/2022/12/steven-weeks-pdTi4_gxSsY-unsplash-1.jpg" url: "https://nerd-notes.com/linear-momentum-in-10-minutes/" date_modified: "2025-05-16T11:50:09+00:00" --- # Linear Momentum Speed Review ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/linear-momentum-in-10-minutes/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/linear-momentum-in-10-minutes/ ### What is momentum? *Anything* that has mass (which is pretty much everything) AND has velocity has momentum. Hence the equation \(p = mv\). Conservation of Momentum Means that the initial momentum value should equal the final. If they are not equal then momentum is NOT conserved and there has been an impulse caused by an external force (more on this later). Conservation of momentum: \[p_i = p_f \] To solve problems add up the momentums’ of objects before a collision. Then set it equal to the sum of momentum of the objects after a collision. ### Three Types of Collisions: 1. **Elastic** – Objects collide and bounce of each other (energy is generally conserved in this type of collision) 2. **Inelastic** – Objects collide and stick to each other. 3. **Explosion** – Object starts at rest then explodes outwards in multiple pieces. Momentum is conserved in ALL collision. Energy, however, might not be conserved. Why? When objects collide a small about of heat is dissipated and lost to the surround environment. ### Example of Conservation Let’s try the following problem: A \( 0.450 \) \( \text{kg} \) ice puck, moving east with a speed of \( 3.00 \) \( \text{m/s} \), has a head-on collision with a \( 0.900 \) \( \text{kg} \) puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision? **Step one:** Identify if momentum is conserved. This problem deals with a elastic collision, so momentum is definitely conserved. Therefore, we can use conservation of momentum **Step two:** Apply conservation of momentum (\( P_i = P_f\)) \[(0.450)(3.00) = (0.900)(v_1) + (0.450)(v_2) \] **Step three:** notice how you have too many unknowns to be able to solve this problem. You need a second equation. This will come from the [conservation of energy](https://nerd-notes.com/energy-in-10-minutes/) (we can use this because the collision is elastic): \[(0.450)(3.00)^2 = (0.900)(v_2)^2 + (0.450)(v_1)^2\] **Step four:** rearrange and solve the equations above. Use any method that works best for you. I would recommend substitution in this case. **Step five:** Final solution: \( v_1 = -1 \, \text{m/s} \) (west), \( v_2 = 2 \, \text{m/s} \) (east) ### Impulse Impulse is a *change in momentum*. This means that \(P_i \neq P_f\). \[\text{Impulse} = \Delta p = m \Delta v = Ft \] The equations above show: the change in momentum, which is really a change in velocity, comes from an external force being applied. This makes sense since a force implies an acceleration, which is a change in velocity. What is an *external* force? It is a force that is not within the system. For example, imagine a car traveling. The system is just the car. Suppose it hits a wall and comes to a stop. The wall applied an external force, that caused a change in velocity, thus a change in momentum. ### Example Impulse Problem A \( 0.0600 \) \( \text{kg} \) tennis ball is traveling at \( 30.0 \) \( \text{m/s} \). After being hit by the opponent’s racket, the ball’s velocity is \( 20.0 \) \( \text{m/s} \) in the opposite direction. Calculate the: a) change in the ball’s momentum and b) average force exerted by the racket if the ball and racket were in contact for \(0.0400\) \(\text{s}\) **Solution**: 1. Check if momentum is conserved. It is NOT conserved in this problem, since the racket is applying an external force. Hence, we will use the Impulse theorm to solve this. 2. Re-arrange and apply Impulse equations: \( \Delta p = m\Delta v \rightarrow (0.060)(30 + 20) = 3\,\text{N}\cdot\text{s} \) (make sure to apply signs correctly, as this is one of the most common mistakes) 3. Solve the part (b) by apply the other equation for impulse. \( \Delta p = Ft \rightarrow 3 = F(0.040) \rightarrow F = 75\,\text{N} \) ### Other Important Concepts for the AP Exam 1. Velocity of center of mass. As long as momentum is conserved, so will the velocity of the center of mass. 2. Collisions at angles. Apply the same laws and equations as collisions in one dimension, but this time split velocity into x and y components and apply conservation in both directions. That’s a wrap! If you are still having difficulty applying these concepts be sure to ask you teachers or friends for guidance. If you want quick and easy guidance, consider [hiring a tutor here](https://nerd-notes.com/product/1-to-1-elite-physics-tutoring/)! Nerd-Notes guarantees a boost in grades and understanding in just the first lesson. ### 10 Problems to Help You Master Momentum! If you get all of these right, you have reached mastery. If you score anything below a 70% — you may want to review concepts or problem solving strategies in detail. [Open in UBQ](https://nerd-notes.com/ubq/22794/) Question 1 Advanced Mathematical A bullet of mass \(0.0500 \, \text{kg}\) traveling at \(50.0 \, \text{m/s}\) is fired horizontally into a wooden block suspended from a long rope. The mass of the wooden block is \(0.300 \, \text{kg}\) and it is initially at rest. The collision is completely inelastic and after impact the bullet + wooden block move together until the center of mass of the system rises a vertical distance \(h\) above its initial position. Part (a)3 pts Calculate velocity of the bullet + wooden block just after impact. Part (b)3 pts Calculate the vertical distance \(h\) reached by the bullet and wooden block. Part (c)3 pts Which of the following two would have the greater effect on the height of the bullet block system: (i) doubling the bullet’s velocity (ii) doubling the bullet’s mass (iii) Neither. Justify your answer. Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22795/) Question 2 Beginner Mathematical A child (\(m = 32 \, \text{kg}\)) in a boat (\(m = 71 \, \text{kg}\)) throws a \(7.1 \, \text{kg}\) package out horizontally with a speed of \(12.2 \, \text{m/s}\). Calculate the velocity of the boat immediately after, assuming it was initially at rest. Ignore water resistance. Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22793/) Question 3 Beginner Mathematical A pool cue ball, mass \(0.7 \, \text{kg}\), is traveling at \(2 \, \text{m/s}\) when it collides head-on with another ball, mass \(0.5 \, \text{kg}\), traveling in the opposite direction with a speed of \(1.2 \, \text{m/s}\). After the collision, the cue ball travels in the opposite direction at \(0.3 \, \text{m/s}\). What is the velocity of the other ball? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22800/) Question 4 Intermediate Mathematical A baseball, mass \(0.5 \, \text{kg}\), is traveling to the right at \(32.2 \, \text{m/s}\) when it is hit by a bat and travels the opposite direction at \(72.2 \, \text{m/s}\). The bat hits the ball with a force of \(1,222 \, \text{N}\). What is the ball’s change in momentum and how long was the ball in contact with the bat? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22802/) Question 5 Advanced Mathematical A \(4 \, \text{kg}\) mass is traveling at \(10 \, \text{m/s}\) to the right when it collides elastically with a stationary \(7 \, \text{kg}\) mass. The \(7 \, \text{kg}\) mass then travels at \(2 \, \text{m/s}\) at an angle of \(22^\circ\) below the horizontal. What is the velocity of the \(4 \, \text{kg}\) mass? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22807/) Question 6 Advanced Mathematical A \(3800 \, \text{kg}\) open railroad car coasts along with a constant speed of \(8.60 \, \text{m/s}\) along a level track. Snow begins to fall vertically and fills the car at a rate of \(3.50 \, \text{kg/min}\). Ignoring friction with the tracks, what is the speed of the car after \(90 \, \text{min}\)? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22810/) Question 7 Advanced Mathematical A \(2,000 \, \text{kg}\) car collides with a stationary \(1,000 \, \text{kg}\) car. Afterwards, they slide \(6 \, \text{m}\) before coming to a stop. The coefficient of friction between the tires and the road is \(0.7\). Find the initial velocity of the \(2,000 \, \text{kg}\) car before the collision? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22812/) Question 8 Advanced Conceptual Consider the following cases of inelastic collisions. Case (1) – A car moving at \(75 \, \text{mph}\) collides with another car of equal mass moving at \(75 \, \text{mph}\) in the opposite direction and comes to a stop. Case (2) A car moving at \(75 \, \text{mph}\) hits a stationary steel wall and rolls back. The collision time is the same for both cases. In which of these cases would result in the greatest impact force? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22815/) Question 9 Intermediate Conceptual A bowling ball moving with speed \(v\) collides head-on with a stationary tennis ball. The collision is elastic and there is no friction. The bowling ball barely slows down. What is the speed of the tennis ball after the collision? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/linear-momentum-in-10-minutes/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/linear-momentum-in-10-minutes/