Newton

Also called N

The SI unit of force, symbol N, equal to one kilogram meter per second squared. One newton is the net force that gives a 1 kg mass an acceleration of 1 m/s squared, and a 1.0 kg object weighs 9.8 N near Earth's surface.

1\ \text{N} = 1\ \frac{\text{kg}\cdot\text{m}}{\text{s}^2}

The base units come straight from $\vec{F}_{\text{net}} = m\vec{a}$ : multiply a mass in kilograms by an acceleration in meters per second squared and the product is in newtons. Every AP Physics table of information lists it in the UNIT SYMBOLS box as newton, N.

How big is one. Roughly the weight of a 100 g object at Earth's surface, since $(0.100)(9.8) = 0.98$ N. A 1.0 kg textbook presses down with 9.8 N. Forces in AP problems mostly run from a few newtons to a few hundred.

The constants box prints it two ways. All four sheets give the magnitude of the acceleration due to gravity at Earth's surface as $g = 9.8\ \text{m/s}^2$ and the magnitude of the gravitational field strength as $g = 9.8\ \text{N/kg}$ . Those are the same unit written differently: $1\ \text{N/kg} = 1\ \text{m/s}^2$ .

Where it goes wrong. A mass in kilograms is not a weight in newtons. "The block weighs 5 kg" needs converting to 49 N before it can enter a force equation, and dropping that step is the most reliable way to be off by a factor of $g$ . Watch the compounds too: $\text{N}\cdot\text{s}$ is impulse, $\text{N}\cdot\text{m}$ is work or torque, and $\text{N}/\text{m}$ is a spring constant.

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