Section 4.2: Linear Momentum
Linear momentum is a measure of an object's motion, defined as the product of its mass and velocity. It is a vector quantity.
Linear Momentum:
\( \vec{p} = m \vec{v} \)
- \( m \): Mass of the object
- \( \vec{v} \): Velocity of the object
Newton's second law in terms of momentum: \( \vec{F}_{\text{net}} = \frac{d\vec{p}}{dt} \)
Example 1
A 2 kg object moves with a velocity of 3 m/s. Find its momentum.
\( \vec{p} = m \vec{v} = 2 \times 3 = 6 \, \text{kg·m/s} \)
Example 2
A 5 kg ball moving at 4 m/s collides with a wall. Find the momentum before collision.
\( \vec{p} = m \vec{v} = 5 \times 4 = 20 \, \text{kg·m/s} \)
Practice Problems
- A 3 kg object moves at 6 m/s. Compute its linear momentum.
- A 10 kg cart moves at 2 m/s. Find the momentum.
- An object of mass 4 kg has momentum 12 kg·m/s. Determine its velocity.
- A 7 kg particle moves with velocity 5 m/s. Find its momentum.
- An object of mass 8 kg slows from 6 m/s to 3 m/s. Find the change in momentum.