An object moving along a straight line has v = -7 m/s. What does this velocity say?
Two lab carts run along one straight track. One moves right at 2.5 m/s; the other moves left at 2.5 m/s. Their speeds match, and their directions do not.
One signed number can say both how fast and which way. How are the signs chosen?
You have seen this move in one-dimensional motion: a velocity is written as one signed number, and the sign tells the direction.
The same choice carries over to momentum, because momentum points the way the velocity points.
Choose one direction along the line as positive, and state it. Either choice is legal.
Making that one choice, and giving every velocity and momentum in the problem its sign from it, is called the sign convention.
Take rightward as positive. The rightward cart has v = +2.5 m/s, and its momentum is positive.
The leftward cart has v = −2.5 m/s. Multiply by its mass, and its momentum comes out negative.
For example, a 2.0 kg ball moving left at 4.0 m/s has v = −4.0 m/s, so p = 2.0 × (−4.0) = −8.0 kg·m/s.
The sign is direction, not size: −8.0 kg·m/s is as much momentum as +8.0 kg·m/s, pointed the other way.
Taking rightward as positive, a cart moves left along a track. What is the sign of its momentum?
Taking eastward as positive, a dog runs west at 6.0 m/s. Which is the dog's velocity?
The line can run any way: left-right along a track, or up-down for a falling ball. Choose the positive direction once, state it, and keep it for the whole problem.
Taking upward as positive, Celia writes a falling ball's velocity as −5.0 m/s. Is her sign correct?
Taking eastward as positive, a 3.5 kg wagon rolls west at 2.0 m/s. Write its velocity and its momentum with their signs.
Write down the values:
m = 3.5 kg, v = −2.0 m/s (westward motion, with east positive), p = ?
Write down the equation:
p = mv
Substitute in the values, and calculate:
p = 3.5 × (−2.0) = −7.0
v = −2.0 m/s and p = −7.0 kg·m/s.
The same wagon, with westward chosen as positive instead. What changes?
The wagon still rolls west at 2.0 m/s.
With westward positive, its velocity is +2.0 m/s and its momentum is +7.0 kg·m/s.
The motion did not change; only the signs describing it changed.
Either convention is legal. State the choice, then keep it.
Taking northward as positive, which mover has a negative momentum?
Taking rightward as positive, a 1.5 kg cart moves left at 2.0 m/s. Enter its momentum in kg·m/s, including its sign.
A bus drives west at 10 m/s. Anouk records its motion taking eastward as positive; Bastian records the same motion taking westward as positive. What sign does the bus's momentum carry in each record?