LECTURE-1

UNITS AND DIMENSION ::

Why do we need units ?

We need units because we want to measure theAmount or quantity of some things. To make thismeasurement globally acceptable we need to put

someUnique measurement value. This value is called a

UNIT

Dimensions are physical quantities like length, mass, time which

Uniquely characterises an object.If say you want to measure the distance then its dimension

is the Length. For matter its mass and for clock it’s the timeUnits are used to measure this physical quantities.Meter for example is the metric unit for length

Units are of two types----1. Metric system (European and other countries)2. Foot-Poundal system (USA)

What are dimensions ?

If you are measuring a very big quantity then you represent your

Measure with a bigger unit.

For example take length of a stick and the distance between OKcity and Stillwater. The first one you can measure with a unit asSmall as meter, What about the second one ?If we want to measure the distance in meters(m) or foot(ft) it is fine but itIs going to be a very big number. Rather it will be easy to represent the distance in tems of a bigger Unit called KILOMETER(Km) or in MILES (miles)

Units can be small and big…

How big or small can a Unit be ??

A unit can be as big as 26,000 Light years, where

1 Lightyear = Distance travelled by Light in 1 year

= 3x108 x60x60x24x365 m

= 3.942x1014 m It’s a large distance !!!!

26,000 Light year is the distance between Sun and the

center of our Galaxy the MILKY WAY.

So we see that Light year is a very big unit as compared

to meter though they both represent length

Let us now see how small a unit can be,If we ask the question as to what is the radius of anAtom, the smallest unit of matter ?The answer is a few angstrom ~ 10-8 m Or that is ~ 0.00000001 mHence we see that the span of measurable quantityhaving same dimension for example length can be veryWide. So we require convenient units while measuringbig or small quantities

1 Km = 1000 m1m = 100 cm (centimeter)1mile = 5280 ft1ft = 12 inch1inch =2.54 cm

The relation between the unit of length in metricSystem.And the foot-poundal system is ::

1 ft = (12×2.54)/100.0 = 0.30 m

1 m =100.0/(2.54×12.0)= 3.28 ft

8

List of some Units and their conversion from metric to foot-poundal systems

USA units Metric Units Metric Units USA units

Inch 2.54 cm Cm 0.39 feet

Foot 30.48 cm m 3.28 feet

Yard 0.91 m m 1.09 yards

Miles 1.61 km km 0.62 miles

For Mass

USA units Metric Units Metric Units USA units

Ounce 28.35 grams Grams 0.035 ounce

Pound 0.45 kilograms

Kilograms 2.21 pounds

UK ton 1.02 metric tons

Metric tons(1000)

0.98 UK tons

US ton 0.91 metric tons

Metric tons(1000)

1.10 US tons

Prefix for UnitsPrefix Symbols Inwords Shift points

micro µ A millionth 6 to right

milli m A thousandth 3 to right

centi c A hundredth 2 to right

deci d A tenth 1 to right

deca da ten 1 to left

hecto h A hundred 2 to left

kilo k A thousand 3 to left

mega M A milliom 6 to left

Some Units in Mechanics

Some Units in Electricity and Magnetism

Some Abbrevetions

s = second N = newton V = volt cm = centimeter lb = pound Ω = ohm m = meter J = joule W = watt ft = foot Hz = hertz A = Ampere g = gram mi = mile C = coulomb kg = kilogram

Some Exercises:

• What is 1 inch in terms of a Km ?• 1 liter is equal to how many meters ?• 1 mile is how many meters ?• What is a light year in terms of meters ?• 1 kilogram is equal to how many ounces ?• What is a milli second ?• 1 pound is equal to how many grams ?• How many seconds have you lived till today on earth ?

LECTURE-2

MOTION

MOTION

02CO, p.14

Describing motion

Any object moving is said to be in motion.Motion is signified by change in position of an

object with timeThere are different types of motions:• Linear --- moving in a straight line• Circular --- moving in a circle• Helical --- going forward while moving in a circle• Wave and Vibrations ---- ripples in waterand many more…..

Helical Motion

How fast do you drive ??Say you are driving back home from school, If somebody ask you this question what will be youranswer ? To answer this you need to know how long you have gone ,that is how far have you travelled and thetime you spent to do so…Comon !!! Why to do all this we have the

speedometerright ??True but it actually measures something called speed

ofyour motion and we will talk about this now..

Speed Speed is a measure of how fast you are moving.There are two types of speed • Average Speed• Instantaneous SpeedSo what is an average speed ?It is defined as the total distance you travelled dividedby the total time it took to travel.Didn’t make any sense right ?? (even if it did I am

goingto do this example folks !)Lets go a bit further with an example

Average Speed

d1 d2

d3d4

Let d1, d2, d3, d4 be 4 different distances travelled in time t1 ,t2 ,t3,t4.

then the average speed is given by

S = (d1+d2+d3+d4)/(t1+t2+t3+t4)

Instantaneous Speed

As the name says this is speed of an object or body at a

particular instant of time.

It is same as average speed for a small time interval.

So if we ask what is the instantaneous speed at say

point A

d1 d2

d3d4

A

We will try to figure it out by looking for a small distance traveled about A for a small time

Hence Instantaneous speed is

Sn|A = Small Distance about A/time spent

The speedometer of a car shows us its instantaneous speed , not the average.

• Tom Travels a distance of 10 meters, if the time taken by him to travel this distance is 40 seconds. Find the Average speed in m/s and Km/hr and mile/hr

• Let us assume that Tom went from P to L then from L to S. If D1=100 m, T1=25 sec is distance and time he took to go from P to L respectively , D2 =150 m, T2=50 sec is distance and time he took respectively to go from L to S. Find Toms average speed for each part of his journey and the total average speed for the whole journey.

2D Graph 1

Time

0 2 4 6 8 10 12 14 16 18

Dis

t

0

2

4

6

8

10

12

14

16

18

Dist Vs Time

Instantaneous Speed can be calculated from a Distance

vs Time graph like the one shown in the earlier slide. If for example someone ask you what is instantaneousvelocity at Distance = 8 m ?

• In the graph draw a line connecting 8 mark on thevertical axes to the straight line. Now from the pointwhere it cuts the straight line drop a line to thehorizontal axis below. You can figure out the time.Divide the distance with this time and you get yourinstantaneous speed.

Example of Instantaneous Speed

p.18

We have been talking about speed, what if The moving object is also changing directions

?We have experienced this--- a car making a turn It changes direction, while movingSo do we have something to define this kind of motions ?

Yes we do have ! VELOCITY , this is a quantity which

by definition gives you both speed and the direction

Velocity is defined as:

Where ∆ is a greek symbol delta used in physics todenote change in a quantity. So ∆x is not delta timesx it rather just sigifies a change in quantity x. Similarly for t. Velocity is a Vector quantity. This are special type of quantity which have both magnitude and directions. The bar over x signifies that it is also a vector quantiy called Displacement.

t

xv

So what is the difference between speed andVelocity ?Speed is the measure of how fast a object is going but Velocity give the direction along which the object is going with the measure of how fast it is going. Example: car is going at 60 mph towards east. The quantity Displacement is different from distance asDisplacement have a sense of direction hidden in it whereas distance is just the measure of how far you went.

LECTURE-3We are quite familiar with this term, we always speak

ofhow fast a car accelerates in compare to other, but what does it actually means Physically ??

Acceleration is a measure of how quickly you can change your velocity. It is also a Vector quantity andhave both magnitude and direction. Another example of acceleration is the motion of a

rollercoasters--- next time when you ride it do think about this..

Acceleration is defined as

When acceleration is along the same direction as the velocity, speed of the object increases. If it is along the opposite direction to velocity speed of the object decreases.

t

va

Fig. 2-4, p.22

Which one of the two sets of Car accelerates??

Example on Acceleration

Consider a car travelling in a highway speeds up from 35 mph to 65 mph in 10 secs time. What is the acceleration ??

Give your answers in mph/s, km/s2 and m/s2

Falling bodies

We have been talking till now about bodies moving along the horizontal direction. What happens when it falls ?Does it change speed ,What about the velocity?Does it Accelerates ??Let us now address all these questions and see what happens to a falling body

Initially• Speed zero• Velocity zero• Acceleration is zero

In between• Speed increases• Velocity increases• Body accelerates

As it reaches the ground• Speed is zero• Velocity is zero• Acceleration is zero

Free Fall

A body is said to be falling freely if it falls

through zero air resistance and was not given any initial velocityFor example dropping a ball through a pipe from which air has been removed Under free fall all bodies have the same acceleration , 9.8 m/s2 or 32 ft/s2

p.24a

p.24b

Free Fall

Who Falls first ?? The elephant or the

feather ??

In free fall objects fall with constant acceleration. Hencetheir Speed changes by the same amount for each time interval.

What if you give an initial velocity to the ball ? For example you throw a ball upward It slows , stop and then fall back. The characteristics of the upward journey is symmetric to the return journey.

Say you throw a ball up with a initial velocity of 29.4 m/s , How long is it

goingto take for the ball to stop ? At whatheight will it stop ? How far have it

fallen while coming down after 2 secs ?