Physics Study Guide/Motion Theory

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Contents

[edit] Introduction

Motion is defined as movement of an object from one place to another place when there is a force applied on the object.

When you push or pull an object to make it move over a distant from rest position

[edit] Speed

If an object travels a distance s over time t then the ratio of distance over time gives Speed of motion

Speed = Distance / Time
v = \frac{s}{t}

[edit] Velocity

The Speed and the direction of travelling can be used to describe the motion and known as Velocity

Therefore, any motion with respect to time can be characterised by Velocity, speed of travelling at any point of time . Velocity of any Motion and can be expressed mathematically as a function of time V(t)

[edit] Distance

From Speed formula above, distance travels

Distance = Velocity x Time
s = vt

[edit] Force

Force, a quantity that sets an object in motion from rest position is directly proportional to object's mass and its acceleration

F = m a

[edit] Work

Work is defined as the ability of a force to set an object in motion or in travelling a distance d from rest position

W = F d = Fp v

When you pull or push an object . The vertical component of force does not do any work or don't have the capability to move object . Only the horizontal component of force has the capability of moving object

Therefore, Work is done on an object when the force applied on object is in the direction of the motion's direction

W = F d cos o

No Work done

W = F d sin o

[edit] Energy

Energy is defined as the ability of a force to set an object in motion over time t

E = \frac{W}{t} = F v

F v cos o is called Kinetic Energy, the energy of a force that makes object to move

F v sin o is called Potential Energy, the stored energy

[edit] Types of Motions

[edit] Linear Motion

Linear Motions refer to all the motions in a straight line without changing direction .

Any motion in a straight line without changing its direction or speed is knowned as Linear Motion with Constant Speed

In Linear Motion with Constant Speed , the speed of travelling is the same at any point of time . Therefore, Velocity and the Distance travelled can be calculated by

V(t) = V
S(t) = V t

Any motion in a straight line without changing its direction at a different speed at different time is knowned as Linear Motion with Changing Speed

In Linear Motion with Changing Speed

at time t1 the speed is v1
at time t2 the speed is v2

Change in Speed v2 - v1 over change in time t2 - t1 indicates change in speed over changing time and this quantity is knownn as Acceleration and is denoted as a

a = \frac{v_2 - v_1}{t_2 - t_1}

Acceleration is used to describe how Speed change over time

  • a > 0, v2 > v1 , Motion with an Accelerating Speed
  • a < 0, v2 < v1 , Motion with Decelerating Speed
  • a = 0, v2 = v1 , Motion without acceleration


v2 - v1 = a [ t2 - t1 ] . With t = t2 - t1 and v = v2 - v1

V(t) = a t
S(t) = V(t) t = a t t = a t2

[edit] Non - Linear Motion

Non - Linear Motions refer to any motions not in a straight line for examples Circular motion, Motion of pendulum, Motion of Spring Up and down left to right with reference to an equilibium point

[edit] Circular Motion

Any object travel on a circle will return to its original starting point . At this point the object travels a distance 2 . If t is the time that it takes to travel distance 2 then the velocity of travelling is

v = 2 / t = 2f with f = 1 / t
s = 2

If an object travels one circle in time t then the velocity and the distance of travelling is

v = 2 / t = 2f with f = 1 / t
s = 2

If an object travels n circle in time t then the velocity and the distance of travelling is

v = n 2 / t = n2f with f = 1 / t
s = n 2

Circular motion is a periodic motion of distance n2


One point that has coordinate (x,y) is equivalent to a point (R,o) on the circle

R2 = x2 + y2
Tano = y / x
y = R Sino
x = R Coso = R Sin (o+90)

Therfore any periodic motion can be represented by a motion that has Amplitude varies with Time, Phase sinusoidally and can be expressed in mathmatical function

F(t,R,o) = R Sin (wt + o)
w = 2f
f = 1 / f

[edit] Formula for non linear motion

If there is a non linear motion motion of V(t) then the change of velocity over the change of time gives the value of acceleration of a linear motion not the value of non- linear motion

If this non linear motion can be divided into the sum of linear motions over time t as long as t in not equal to zero . Then the sum of acceleration of all the linear motions will give the value of the non linear motion

This can be expressed mathematically as

Lim t -> 0 v1 + v2 + v3 + ... = a

The expression above can be written as

a = \frac{dV}{dt}

Another word, accelleration of non linear motion can be calculated from linear motion by

a = \frac{dV}{dt} = Lim t -> 0 v1 + v2 + v3 + ...

From this we have a method of calculating acceleration of non linear motion from linear motion

the same will applied to calculating distance

Lim t -> 0 s1 + s2 + s3 + ... = s

The expression above can be written as

a = \int V dt

Another word, distance travelled of non linear motion can be calculated from linear motion by

a = \int V dt = Lim t -> 0 s1 + s2 + s3 + ...

[edit] Motion Formulas

With any motion either Linearly or non linearly can be expressed as a function of Velocity with Time V(t) then

1) Accleration, Rate of change of speed over time can be calculated by

a = \frac{dV}{dt}

2) Distance travelled, distance travelled with Velocity V(t)

s = \int V(t) dt

3) Force, quantity used to set an object in motion

F = m a = m \frac{dV}{dt}

4) Work Done, the ability of Force to set object in motion

W = F d = Fpv
E = {F}\int V(t) dt

5) Energy, the ability of Force to set object in motion in time t

E = \frac{Fd}{t} = F v
E = \frac{F}{t} \int V(t) dt
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