Concepts of Kinematics

LINEAR MOTIONResearch Scholar L.N.I.P.ETahir Ramzan Bhat

ScalarScalars are quantities that are fully described by a magnitude (or numerical value) alone. Vectors are quantities that are fully described by both a magnitude and a direction.

Distance and displacementMotion is change in position with respect to some frame of reference. (final position minus initial position). The simplest linear motion variable is a scalar called Distance (l). (l) Is the length an object travelled irrespective of direction (mtr, feet etc)

displacementdisplacement is a vector quantity.shows distance and direction of objects.Shortest distance from the reference point.Displacements are calculated as final position minus initial position in that particular direction

Speed and VelocitySpeed is how fast an object is moving without regard to direction. Speed is a scalar quantity like distance. Speed (s) is defined as the rate of change of distance (s = l/t), so typical units are m/s, ft/s, km/hr, or miles/hr.

SpeedSpeed is one way to describe motion. It describes how fast an object is moving using distance and time. Average speed is the total distance traveled over the total time and instantaneous speed is the speed at a particular momentFor example, 30 miles per hour means object travels distance of 30 miles in an elapsed time of one hour. Write as,(SPEED) =

(Distance traveled)(Time elapsed)30 miles per hour = 30 mileshour

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Practice:What is the average speed of a cheetah that sprints 100 meters in 4 seconds? How about if it sprints 50 meters in 2 seconds?

A car has an average speed of 100 kilometers per hour. How far does it travel in 30 minutes?

VelocityConstant speed means steady speed. Something with constant speed doesnt speed up or slow down. Constant velocity means both constant speed and constant direction. Constant direction is a straight line, so constant velocity means motion in a straight line at constant speed.Constant speed and constant velocity are not the same.A body may move at constant speed along a curved path but it does not move with constant velocity, because its direction is changing every instant.

PracticeThe speedometer of a car moving east reads 100 km/h. It passes another car moving west at 100 km/h. Do they have same speed? Velocity?

During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? Constant velocity?

VelocityVelocity is the vector corresponding to speed. V is the speed of an object, in a particular direction.Velocity is the rate of change of displacement (V = d/t), so its units are the same as speed, and are usually qualified by a directional adjective (i.e., horizontal, vertical, ).

VelocityThe phrase rate of change is very important because velocity defines how quickly position is changing in the specified direction (displacement).

AccelerationDefine acceleration as how fast velocity changesAcceleration is a rate of a rate (units will have 2 time values)(ACCELERATION) = (Change in Velocity)(Time interval)

Note: An object accelerates anytime its velocity changes. Examples include:Object speeds up.Object slows down Object changes direction (curved path)Best example of acceleration is objects in free fall

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Equationss = d/tv = d/ta = v/tg = 9.8 m/s/s

GravityMany types of forces act on objects.Gravity is an attractive force between all objects that have mass.

Gravity (cont.)The ball does not travel in a straight line because of the unbalanced force of gravity acting on it.

The Law of Universal GravitationThe Law of Universal Gravitation states that all objects with mass are attracted to each other.

The magnitude of attraction depends on the mass of each object and the distance between them.

The Law of Universal Gravitation (cont.)The gravitational force becomes stronger as either or both objects increase in mass or move closer together.The gravitational force becomes weaker as either or both objects decrease in mass or move farther apart.

InertiaInertia:Mass:Resistance to being acceleratedQuantity of matter an object is made of.measure of the inertia of the object scalar quantitynot the same as weight

Mass Quantity of matter an object is made of.measure of the inertia of the object scalar quantitynot the same as weightMass and Inertialarge mass=lots of inertia small mass=not lots of inertia

rpolesWeightWeight (W) is the attractive force between the earth and any body in contact with it or close to its surface

Product of the mass (m) of the body and the acceleration caused by the attractive force between it and the earth(g = 9.81 ms-2)

i.e.W = m g

Gravity is based on:Mass of bodiesDistance between bodiesrequator

r=radius of earthrequator > rpolesGequator < gpolesWequator < Wpoles

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ForceA push or pull that one object exerts on another object.Examples: Earth (pulls us downward), chairs, pencils.Example: pulling a drawer open; you exert force on the drawer.

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An objects motion changes in response to a force.A force has a size and a directionboth are important in determining an objects motion. The force you exert on the book when you push is called a contact force. A contact force is a force that is exerted when two objects are touching each other.

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Long-Range ForcesA force can be exerted if two objects are not in contact.If you bring a magnet close to a paper clip, the paper clip moves toward the magnet, so a force must be acting on the paper clip.

Long-Range ForcesA dropped ball will fall downward, even though nothing appears to be touching it. The forces acting on the paper clip and the ball are long-range forces.In SI units the unit of force is the Newton, which is abbreviated N and named for Isaac Newton. One Newton is about the amount of force needed to lift a half cup of water.

Momentum:- Is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop. Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum

Momentum can be defined as "mass in motion.

All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.

Momentum = mass velocity

p = m vwhere m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

The standard metric unit of momentum is the kgm/s.

It is going to take more force to move a large mass. Ten pounds is twice as much as five pounds. It will take twice as much force to move 10 pounds as it will to move five pounds. When enough force is applied to move either 10 pounds or five pounds and they were both given the same speed of movement (velocity), the 10-pound weight would have twice as much momentum. Remember that momentum is not just velocity. While momentum is movement, it is made up of both velocity and mass.

For example, it would take more effort (force) on your part to catch the 10-pound weight (twice as much effort) as it would for the five-pound weight if both traveling at the same speed (velocity).

Types of momentumLinearAngular

Linear momentum:- Momentum is the quantity of motion of a body in linear motion. It is equal to the product of the bodys mass and velocity.

That is : momentum = Mass X velocity M = m X v where : m is the mass [Kg] v is the velocity[m/s] M is the momentum[Kg m/s]

Angular Momentum:- The quantity of angular motion possessed by a body is called its Angular momentum. just as linear momentum varies with a varying body mass and varying velocity.

Angular momentum = moment of inertia X Angular velocity H = j X where : j is the moment[Kg.m] is the angular velocity[/s or rad/s] H is the angular momentum [Kg.m./s or Kg.m.rad/s]

Impulse DefinedImpulse is defined as the product force acting on an object and the time during which the force acts. The symbol for impulse is J. So, by definition: J = F t Example: A 50 N force is applied to a 100 kg boulder for 3 s. The impulse of this force is J = (50 N) (3 s) = 150 N s. Note that we didnt need to know the mass of the object in the above example.

Impulse UnitsJ = F t shows why the SI unit for impulse is the Newton second. There is no special name for this unit, but it is equivalent to a kg m /s. proof: 1 N s = 1 (kg m /s2) (s) = 1 kg m /s{Fnet = m a shows this is equivalent to a newton. Therefore, impulse and momentum have the same units, which leads to a useful theorem.

PRESSUREPressure is defined as the distribution of force over a given area. The greater the area over which the force is distributed the smaller the pressure. Snowshoes are an excellent example of how the amount of area is increased to spread out the force and thus decrease the pressure , making it possible to walk on the snow.36

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PRESSURE (Pascals)P = F/AWhere P = pressureF = force(N)A = area(m2)1 pascal = 1 N/ m237

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PROBLEMIf a person who weighs 400N is standing on one foot which has a contact area of 100cm2. What is the pressure exerted?

F = 400NA = 100cm2P=F/A = 400/100 = 4N/cm238

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