Newton's Second Law

If $\Sigma$$\vec{F}$$\ne$ 0 (i.e. there is a net external force acting on an object) then,
 

$$\Sigma \vec{F} \vec{a}$$ (2)

Definition: Inertia is the tendancy of an object to resist any attempt to change its state of motion. Mass is the force required per unit of acceleration produced and is a measure of inertia. Mass is a scalar and has SI units of kilograms (kg). Example: If a bowling ball and a golf ball are hit with a bat, the bowling ball would be much harder to get moving since it has greater mass and thus greater inertia.

Note:

• $\vec{a}$ is inversely proportional to m . This means that, for the same force, a smaller mass will have a larger acceleration.
• Newton's second law is a vector equation which contains three scalar equations (in three dimensions): $\Sigma$F_x = ma_x , $\Sigma$F_y = ma_y , $\Sigma$F_z = ma_z .
• The first law is a special case of the second law.
• The SI unit of force is the Newton (N). Definition: 1 Newton is the force that produces an acceleration of 1 m/s ² when acting on a 1 kg mass. In the cgs system: 1 dyne = 1 g cm/ s ²= 10^{- 5}N. In the British engineering system: 1 pound (lb) = 4.448 N.

Definition: Weight ( $\vec{w}$ ) is the force exerted on an object by a gravitational field. From Newton's second law,

w = mg. (3)

Note:

• Weight is a vector with direction towards the earth's center, or perpendicular to the earth's surface.
• The weight of an object is different on the earth and on the moon since the strength of the gravitational field is different ( g_earth$\ne$g_moon ).
• The value of g varies with distance from the center of the earth (more on this in chapter 7). As a consequence:
  • Since the earth isn't a perfect sphere, the weight of an object varies slightly from place to place on the earth's surface.
  • The weight of an object varies slightly with altitude above the earth's surface.
• In comparison, mass is a scalar with a value independent of location. Notice however that, in the approximation that g is constant, mass is proportional to the magnitude of the weight and the two quantities can be used interchangeably. This is called the equivalence principle.