Scalars & Vectors
Scalars are used to describe one dimensional quantities, that is, quantities which require only one number to completely describe them. Examples of scalar quantities are: Temperature, Time, Speed, Mass.
Vectors are used to describe multi-dimensional quantities. Multi-dimensional quantities are those which require more than one number to completely describe them. Vectors, unlike scalars, have two characteristics, magnitude and direction. Examples of vector quantities are: Velocity, Acceleration, Force.
Mechanics deals with the behavior of moving objects.
Kinematics deals with the study of motion without taking into account the cause of motion.
Dynamics is concerned with the cause of motion, namely force.
- An object is said to be in motion if it changes its position with respect to its surroundings in a given time.
– An object is said to be at rest if it does not change its position with respect to its surroundings.
Types of Motion:
Translatory Motion: In translatory motion the particle moves from one point in space to another. This motion may be along a straight line or along a curved path.
Rectilinear motion: Motion along a straight line is called rectilinear motion. Example: A car moving on a straight road.
Curvilinear motion: Motion along a curved path is called curvilinear motion. Example: A car negotiating a curve.
Rotatory Motion: In rotatory motion, the particles of the body describe concentric circles about the axis of motion.
Vibratory Motion: In vibratory motion the particles move to and fro about a fixed point. Example Simple Pendulum
Distance & Displacement
Distance: The distance covered by a moving object is the actual length of the path followed by the object. Distance is a scalar quantity. SI unit of distance is Metre .
Displacement is the shortest distance covered by a moving object from the point of reference (initial position of the body), in a specified direction. Displacement is a vector quantity. SI unit of displacement is metre.
The displacement is given by a number with proper units and direction.
Uniform Motion: When a body covers equal distances in equal intervals of time then the body is said to describe uniform motion.
Non Uniform Motion: When a body moves unequal distances in equal intervals of time or vice-versa, then the body is said to describe non-uniform motion.
Speed, Velocity & Acceleration
Speed can be defined as the distance covered by a moving object in unit time
Speed = distance / time = s/t where S is the distance covered and t is the time taken.
SI unit of speed is m/s. Speed is a scalar quantity.
Uniform Speed: An object is said to be moving with uniform speed if it covers equal distances in equal intervals of time.
Non-uniform Speed: An object is said to be moving with variable speed or non-uniform speed if it covers equal distances in unequal intervals of time or vice-versa.
Average Speed: When we travel in a vehicle the speed of the vehicle changes from time to time depending upon the conditions existing on the road. In such a situation, the speed is calculated by taking the ratio of the total distance travelled by the vehicle to the total time taken for the journey. This is called the average speed.
Instantaneous Speed: When we say that the car travels at an average speed of 60 km/h it does not mean that the car would be moving with the speed of 60 km/h throughout the journey. The actual speed of the car may be less than or greater than the average speed at a particular instant of time. The speed of a moving body at any particular instant of time, is called instantaneous speed.
Velocity: is defined as the distance travelled in a specified direction in unit time. The distance travelled in a specified direction is displacement. Therefore, velocity can be defined as the rate of change of displacement.
Uniform velocity: A body is said to be moving with uniform velocity if it covers equal distances in equal intervals of time in a specified direction.
Variable velocity: A body is said to be moving with variable velocity if it covers unequal distances in equal intervals of time and vice-versa in a specified direction or if it changes the direction of motion.
Acceleration: When the train starts from rest its speed increases from zero and we say that the train is accelerating. After sometime the speed becomes uniform and we say that it is moving with uniform speed that means the train is not accelerating. But as the train is nearing Mysore it slows down, which means the train is accelerating in negative direction. Again the train stops accelerating when it comes to a halt at Mysore . Acceleration is a vector quantity.
Positive Acceleration: If the velocity of an object increases then the object is said to be moving with positive acceleration. Example: A ball rolling down on an inclined plane.
Negative Acceleration: If the velocity of an object decreases then the object is said to be moving with negative acceleration. Negative acceleration is also known as retardation or deceleration. Example: A ball moving up an inclined plane.
Zero Acceleration: If the change in velocity is zero, i.e., either the object is at rest or moving with uniform velocity, then the object is said to have zero acceleration. Example: a parked car, a train moving with a constant speed of 90 km/hr
Uniform Acceleration: If the change in velocity in equal intervals of time is always the same, then the object is said to be moving with uniform acceleration. Example: a body falling from a height towards the surface of the earth.
Non-uniform or Variable Acceleration: If the change in velocity in equal intervals of time is not the same, then the object is said to be moving with variable acceleration.
Circular motion: Motion along circular track is called circular motion . An object moving along a circular track with uniform speed is an example for a non – uniform motion because the direction of motion of the object goes on changing at every instant of time. Example – A car negotiating a curve with uniform speed A circle can be considered as a polygon with infinite sides and hence motion along a circular path is classified as non-uniform motion.
Force can be defined as a push or a pull. Force is something that can accelerate objects. For example, when you throw a ball, you apply a force to the ball. Force is measured by Newton (N). A force that causes an object with a mass of 1 kg to accelerate at 1 m/s is equivalent to 1 Newton.
Newtons First Law of Motion
Net Force is the sum of all forces acting on an object. For example, in a tag of war, when one team is pulling the tag with a force of 100 N and the other with 60 N, the net force would be 20 N at the direction of the first team (100 N – 60 N = 40 N).
First Law of Motion: An object will remain at rest or move with constant velocity when there is no net force acting on it. This is called Newton’s First Law of Motion, or Law of Inertia. Newton’s First Law deals with an object with no net force.
Newtons Second Law of Motion
When the net force acting on an object is not zero, the object will accelerate at the direction of the exerted force. The acceleration is directly proportional to the net force and inversely proportional to the mass. Newton’s Second Law talks about an object that has net force. It can be expressed in formula
F = ma
Newtons Third Law of Motion
When one object applies a force on a second object, the second object applies a force on the first that has an equal magnitude but opposite direction. In other words, when you kick the wall, the wall kicks you back with equal force. As a result you will get hurt. These forces are called action-reaction forces.
Remember when you kick the wall, you exerts force on the wall. When the wall kicks you back, it exerts force on you. Therefore, the net force on the wall is not zero and the net force on your foot is not zero neither.
Mass & Weight
Mass and weight are different in physics. For example, your mass doesn’t change when you go to the Moon, but your weight does. Mass shows the quantity, and weight shows the size of gravity.
If you know your mass, you can easily find your weight because
W = mg
If your mass is 50 kg on Earth, your weight is
Weight is measured by Newton (N).
Normal force: The normal force acts on any object that touches surface (either directly or indirectly). The normal force would be applied on a ball on a table, but not on a ball in the air, for instance. It always acts perpendicularly to the surface. The formula to calculate the normal force is
FN = – mg
For example, the normal force acting on a 50 kg-person would be
Friction is the force that acts between two object in contact because of action-reaction.
Force of friction can be calculated by the formula
The value of depends on surface you are dealing with. The following table shows some example of .