AP Physics 1 - Unit 2: Force and Translational Dynamics

2.1 Systems and Centre of Mass

Centre of mass: where the mass of a system or an object can be defined

Balance position: average position of all the parts of an object/system

$x_{\operatorname{cm}}=\frac{\sum mx_{i}}{\sum m}$

An object is in equilibrium if:

It remains at rest
It moves at a constant speed in a straight line
It has no acceleration
It has balanced forces

2.2 Forces and Free Body Diagrams

Force: a vector quantity that describes interactions between systems/objects

An object cannot exert a force on itself
only external interactions cause a change & apply a force on a system

There are 2 types of forces;

Contact forces: due to direct contact and includes

Tension Force $F_t$

Normal Force $F_N$

Friction Force $F_f$

Applied Forces

Field forces: exerted without any contact

Gravitational Force $F_g$

Objects can be represented by their centre of mass

Freebody diagrams: used to describe the forces acting on a system visually

If an object isn’t accelerating then $\sum F_{x}=0$ & $\sum F_{y}=0$

$F_N$ ; when two objects touch, they push perpendicular to their plane of contact

2.3 Newton’s Third Law

Newton’s Third Law: All interactions happen in pairs

Pairs in forces of interactions are -

equal in forces
equal/same in kid
opposite in direction

Action-Reaction pair (do not mix this with normal force):

When two objects are pulling or pushing each other, they are sharing a force

The effect of a force of an object depends on its mass

2.4 Newton’s First Law

An object is in equilibrium when:

It remains at rest
It moves at a constant speed in a straight line

During equilibrium forces are balanced

Newton’s First Law states that:

an object at rest stays at rest
an object in motion will always stay in motion unless an external force acts on it

2.5 Newton’s Second Law

Newton’s Second Law states that:

If the forces acting on an object/system are unbalanced the object will accelerate

$a=\frac{\sum F}{m}$

Acceleration is directly proportional to the net force

Acceleration is inversely proportional to the mass

Forces are unbalanced in the direction of the acceleration

An object slows down when the acceleration is in the direction opposite to it’s motion

$\sum F$ : All the forces acting on an object

When An object is attached to a string, it’s acceleration is equal to the tension force

$F_T=a$

$F_{T}$ : The force caused by a pull from a string

2.6 Gravitational Force

Gravitational Force: force of attraction between the centre of mass of two objects

Weight: the gravitational pull experiences

$F_g=mg$

Universal Gravitation:

$F_{g}=\frac{Gm_1m_2}{r^2}$

Gravitational Constant $(G)$ : $6.67\cdot10^{-11}$ Nm²/kg²

Gravity: the strength of the gravitational field not necessarily earth

$g=\frac{Gm}{r^2}$

Mass is always the same unless you are on a different planet

Gravitational Force and Mass are directly proportional

Apparent weight: the different sensation of weight upon acceleration

When the normal force exerted is greater than the gravitational force, you feel heavier and vice vera

Heavier: F_N>F_g

Lighter: F_N<F_g

An object appears weightless if;

There are no forces exerted on it
The force of gravity is the only force applied on the object

Inertia is a measure of how much an object resists motion or acceleration

Mass is the amount of matter in an object

All bits of matter attract each other, that’s what makes up gravity

$w=mg$

$w$ : weight

The higher the inertial mass the harder it is to accelerate the object

Gravitational mass and inertial mass are identical

2.7 Kinetic and Static Friction

Friction: the resistance to motion of an object relative to another

2 Types of Friction;

Static friction: non-sliding or rolling
Kinetic friction: sliding friction

An object can accelerate due to static friction

Static friction can increase but has a maximum

Magnitude of friction is affected by;

Friction Coefficient $\left(\mu\right)$ :

The type of surfaces that are interacting

It’s value depends on the surface

For any surface \mu_{s}>\mu_{k}

Normal Force $(F_N)$ :

$\left\vert F_{f}\right\vert\le\mu\left\vert F_{N}\right\vert$

Only for Kinetic friction

Coefficient of friction is unit-less because it is a ratio

2.8 Spring Constant/Forces

Spring Constant $(k)$ : a property of a spring that determines how stiff it is

To determine a spring force:

Hooke’s Law, $F_s=-kx$

When Springs are connected:

Uniform series, $\frac{1}{k_{t}}=\frac{1}{k_1}+\frac{1}{k_2}$

Parallel attachment, $k_t=k_1+k_2$

Spring Forces are exerted in the opposite direction to the displacement from equilibrium

2.9 Circular Motion

In order for an object to accelerate it must experience a non zero net force

Centripetal acceleration: acceleration pointed towards the centre, always a result of a net force

Tangential Speed during centripetal acceleration:

$v=\frac{2\pi r}{t}$

Centripetal force isn’t it’s own force and CANNOT be referred to as $F_c$

Forces parallel to the velocity of an object will cause it to speed up or slow down

Forces perpendicular to the velocity of an object will cause it to change directions

Tangential acceleration: the rate at which an objects speed changes

Objects that follow the laws of circular motion do not always have to be a complete circle

$a_{c}=\frac{v^2}{r}$

Force is directly proportional to the mass
Force is directly proportional to the velocity
Force is inversely proportional to the radius