MOTIONHow do objects move and how do we

explain it

What is Motion? What is Motion and what is not? The Position Vector Trajectory versus Displacement What is Speed? What is Velocity? Linear Motion Nonlinear Motion Uniform Motion (UM)

A Guide to Motion

Accelerated Motion What is Acceleration? Accelerated Motion Equations The UAM Graphs A Graphic Problem Free Falling Objects And now… one Question to Explain Circular Motion A Very Funny Motion

A Guide to Motion

What is Motion?

Are these aircrafts moving? How can we know it?

What is Motion?

Are these ships moving? How can we know it?

Motion is change in an object’s position along time

The idea needs a definition of position as the distance to some reference frame (a point or axis)

When position is fixed… MOTION IS ALWAYS RELATIVE

EVERY OBJECT MOVES REGARDING TO ANY POSSIBLE REFERENCE FRAME

Absolute motion or absolute rest make no sense at all, THEY ARE IMPOSSIBLE

What is Motion and what is not?

This is a 2D vector (a plane or flat vector)

The vector goes from an origin position (0,0) to the point expressed as (4,3)

It means that the object placed at the end of the vector (the arrow’s end) is 4 units away from axis OY and 3 units away from axis OX

We usually express a vector either with a small or a capital letter (here “v”) with a little arrow at the top

The Position Vector

While trajectory is the path taken by a mobile along time, displacement is the vector that expresses the shortest distance between the origin and the end and also the direction taken by the moving object

Trajectory versus Displacement

Kinematic magnitude that measures which mobile is faster, i.e., which mobile covers its path first or runs a longer distance in the same time interval. It is a scalar quantity defined as the distance covered divided by the time interval. If we define it for a given interval, then we find the average speed

IS Unit : m/s (meters per second)

What is Speed?

Kinematic magnitude defined with a vector that measures a mobile’s speed taking into account not only its quantity but also the direction in which the mobile runs. Velocity and speed must not be confused, because speed is only the velocity quantity without any direction. Velocity can also be simply defined as the displacement (a vector quantity that has a direction too) divided by the time interval.

IS Unit : m/s (meters per second) just like speed

What is Velocity?

A mobile that holds a straight-line path and follows no curves has a linear motion

Linear Motion

A mobile that takes a curved path has a nonlinear motion. According to the particular form of the curve, it can be circular, parabolic, elliptical, etc.

Nonlinear Motion

A mobile that runs at a constant speed, i.e., that covers equal distances in equal time intervals has a uniform motion

Equation to describe uniform motion in one dimension only:

x = x0 + v · (t – t0) It is a degree 1 equation, a linear equation when

represented on a graph (x versus t is a straight line) SLOPE or gradient is the vertical change divided by

the horizontal change for any part of the line (Here: Dx/Dt = v)

A positive slope means that velocity is positive too, and a negative slope means that velocity is negative

Uniform Motion (UM)

A mobile with a non constant velocity, for it changes in a time interval, has an accelerated motion

Then we say the mobile has got an acceleration

If it runs with a constant acceleration then we say that it has a uniformly accelerated motion (UAM)

Accelerated Motion

Kinematic magnitude defined as the rate at which the velocity is changing, due to changes in speed and/or direction. As a scalar quantity it can be defined by the difference between final velocity and initial velocity, divided by the time interval

IS Unit : m/s2 (meters per second each second)

What is Acceleration?

Motion in one dimension has an equation to calculate velocity (which is not constant) :

v = v0 + a · (t – t0)

It is a degree 1 equation, a linear equation when represented on a graph (v versus t is a straight line)

A positive slope means that acceleration is positive too, and a negative slope means that acceleration is negative

There is another equation to calculate position:

x = x0 + v · (t – t0) + ½ a · (t – t0)2

It is a degree 2 equation, a quadratic equation when represented on a graph (x versus t is a curve called parabola)

Accelerated Motion Equations

The UAM Graphs

A Graphic Problem

What kind of motion has this mobile?

When we drop an object and let it fall free it holds an accelerated motion. In fact this motion has a constant acceleration (UAM)

Near to the Earth surface, falling acceleration is constant and it is approximately 9.8 m/s2

The value is known as GRAVITY ACCELERATION and it depends on the mass and size of our planet, that is why it has different values for each planet

For example, in the Moon objects fall with a gravity acceleration of 1.6 m/s2

Free Falling Objects

And now…one Question to Explain

A special curved path is a circumference. Its particular feature is that IT HAS A CONSTANT RADIUS, so its lengths equals: L = 2·p·r

A special case of circular motion is UNIFORM CIRCULAR MOTION (UCM)

A mobile holds a UCM when it has a CONSTANT ROTATIONAL SPEED (sometimes called ANGULAR SPEED and symbolized as w)

w is defined as: w = Dj/Dt and is measured in rad/s

Relation between rotational (w) and linear or tangential (v) speed: v = w·r

Circular Motion

A Very Funny Motion

where different passengers have a different speed... or not?

We usually describe this motion saying that THEY TURN AROUND and do SOME REVOLUTIONS PER MINUTE

(r.p.m.), where 1 rpm equals 2p/60 rad/s