Momentum is a term you’ve likely heard used in everyday language that also has a special meaning in physics. When a sports team is described as having “momentum”, you know that the team is on a winning streak and hard to stop. Momentum in physics has a similar but more precise meaning. This post will explain what momentum is, the equation for momentum, and how to calculate momentum.  

What Is Momentum In Physics?

Definition Of Momentum

In Physics, momentum is a quantity of motion that applies to moving objects. Every object that is in motion has momentum. As we’ll explain in further detail below, how much momentum a moving object has depends on its mass and velocity. 

How Momentum Relates to Velocity and Mass

Momentum is the product of an object’s mass and velocity. This means that momentum is directly proportional to both mass and velocity. The larger the mass of the object, the more momentum it has. Similarly, for velocity, objects that are moving faster also have more momentum. 

For example, a heavy truck traveling on the highway has more momentum than a smaller car traveling at the same speed because it has a greater mass. Having more momentum also makes it harder for the truck to stop. 

An object’s momentum can also change as its motion changes. For example, a child sledding down a steep hill gets faster and faster as they slide down. As the child’s velocity increases, they also gain momentum.  

Check out this video from Conceptual Academy for more examples of momentum. 

Momentum Units

The units for momentum come from the equation for momentum and the fact that momentum is the product of mass and velocity. The standard units for mass are kilograms (kg) and the units for velocity are meters per second (m/s). Therefore, momentum is measured in units of \text{kg}\cdot\text{m/s}. 

Is Momentum a Vector?

As a reminder, vectors are quantities that have both a magnitude and direction. As you’ll recall from your study of kinematics, velocity is a vector quantity because it tells you both how fast an object is moving and the direction it is moving in, such as 25\text{m/s} East. Since momentum depends on velocity, momentum is also a vector.  

How To Calculate Momentum

Equation for Momentum

The equation for momentum is:

…where:

• p is momentum
• m is mass
• v is velocity

Step-By-Step Guide for Using the Equation for Momentum

When using this equation to calculate momentum, you’ll want to take the following steps:

1. Identify the mass, in kilograms.
2. Identify the velocity, in meters per second. 
3. Substitute these values into the equation p=mv.
4. Solve by multiplying the mass and the velocity. 

For example, say a problem asks you to calculate the momentum of a 15\text{ kg} object moving at 6\text{ m/s}\text{ North}. Applying the steps above produces:

1. The mass, m, of the object is 15\text{ kg}.
2. The velocity, v, of the object is 6\text{ m/s}\text{ North}.
3. Substituting these values into the momentum equation gives: p=(15\text{ kg})(6\text{ m/s}\text{ North}).
4. Multiplying mass and velocity gives: p=90\text{kg}\cdot\text{ m/s}\text{ North}.

How To Find Momentum Using Examples

Applying the Equation for Momentum to Real-World Situations

We can find momentum in a variety of real-world situations whenever we know mass and velocity. 

For example, if you are a baseball catcher, you might be curious about the momentum of the fastballs you catch. The average fastball pitch is around 90\text{ mph} or 40\text{ m/s}. The mass of a baseball is about 5\text{ ounces} or 0.145\text{ kg}. Substituting these values into the momentum equation produces:

p=mv=(0.145\text{ kg})(40\text{ m/s})

p=5.8\text{ kg}\cdot\text{m/s}

Another real-world example where momentum has important applications is with cars. Cars often have a large amount of momentum due to their large mass and the ability to move at high velocities. And when a car has a lot of momentum, it can be harder for it to come to a stop in an emergency or accident. For example, an average-sized car can have a mass of about 1{,}800\text{ kg}. If the car is traveling at 32\text{ m/s}, (about 60\text{ mph}), its momentum is:

p=mv=(1{,}800\text{ kg})(32\text{ m/s})

p=57{,}600\text{ kg}\cdot\text{ m/s}

Momentum Experiments

You can see momentum in action, and calculate momentum, in a variety of experiments. To calculate the momentum of an object in an experiment, you will need a scale to measure the object’s mass, a ruler to measure distance, and a stopwatch to measure the time. By measuring the distance and time an object travels, you can calculate its velocity using the formula: v=\frac{d}{t}. 

For example, you can do an experiment at home by rolling a ball down a ramp and having it hit a stationary object. You’ll notice that the steeper the ramp is, the more velocity and momentum the ball has, and the bigger impact it has on the stationary object it hits. If you compare two balls with different masses rolling down the same ramp, they have the same velocity but the heavier ball has more momentum and a bigger impact on the object it hits. 

Conclusion

Momentum is a quantity of motion that depends on an object’s mass and velocity. You now know how to calculate the momentum of any object and can apply this to find momentum in many everyday situations. As you’ll learn in future posts, knowing how to calculate momentum can provide important insights into collisions and forces.