The UPSC mains GS-3 paper syllabus has various subjects like Economics, Science and Technology. Science and technology in UPSC is mostly concerned with current Affairs. but it is necessary to understand the basics of science.
- Laws of Motion
LAWS OF MOTION
Newton’s First Law of Motion
- Newton’s first law of motion says that a body continues to be in its state of rest or in uniform motion along a straight line unless an external force is applied on it. This explains:
- Why when a beat a carpet with stick, dust particles separate out of it.
- Why passengers feel sudden jerk forward when a moving Bus or train stops suddenly.
Newton’s Second Law of Motion
- Newton’s second law of motion says that the rate of change of linear momentum is proportional to the applied force and change in momentum takes place in the direction of applied force. This explains:
- Why it is easier to push empty cart than full cart
- Why adult is able to push or pull a cart easily than a child
- The second law of motion is called real law of motion because first and third laws of motion can be obtained by it.
Newton’s Third Law of Motion
- Third law of motion says that “For every action there is an equal and opposite reaction and both acts on two different bodies.” Swimming is possible because of this law. This explains why jerk is produced in a boat when bullet is fired from it. A person is hurt on kicking a stone due to reaction only.
Law of Conservation of Linear Momentum
- This law says that if no external force acts on a system, then its total linear momentum remains conserved. In equation form, Momentum=mass*velocity. To increase the momentum of an object, we need to either increase its mass or velocity or both.
- Rockets work on law of conservation of momentum. As momentum in one direction is given to the rocket’s exhaust gases, momentum in the other direction is given to the rocket itself.
- Weight (w)
- Weight refers to a force with which a body is pulled towards the centre of the earth due to gravity. It has the magnitude mg, where m is the mass of the body and g is the acceleration due to gravity, thus w=mg
- When a lift is either at rest or moving with a constant speed, then apparent weight of a person standing in it is equal to his actual weight. Thus, R = mg
- When a lift is accelerating upward, then apparent weight would be R1=M(g+a). Thus weighing machine would read the apparent weight more than the actual weight.
- When a lift is accelerating downward, then apparent weight would be R2=m(g-a). Thus, the weighing machine would read less than actual weight.
- When the lift is falling freely under gravity then apparent weight R3=m(g-g) =0. In this case, machine will read zero.
- If lift is accelerating downward with an acceleration greater than g, then the person will lift from floor to the ceiling of the lift.
- Friction is force acting on the point of contact of the objects, and which opposes the relative motion. Friction always works parallel to the contact surfaces. Frictional forces are produced due to intermolecular interactions acting between the molecules of the bodies in contact.
- There are three kinds of friction viz. static friction, limiting friction and Kinetic friction.
- Static friction is the opposing force which works when one body tends to move over the surface of the other body but actual motion is not taking place. This makes harder for two objects to slide alongside one another. Glass on Glass is an example of static friction. Static friction results from the interlocking irregularities present on the two surfaces in contact. This force will increase in response to an attempt to move the objects until it is overcome at the threshold of motion. The maximum value of static friction when body is at the verge of starting motion is called Limiting Friction. The friction that occurs after the point where motion is achieved is referred to as kinetic friction.
Common examples of Friction:
- We can hold a pen while writing due to the force of friction. Friction is needed in this case for better grip. If there is no friction, it would be really difficult to write.
- If there was no friction, walking on the road would become impossible. It is friction that allows us to walk.
- After a shower, it becomes difficult to drive a car at high speed on the wet road because friction decreases.
- Angle of sliding or angle of repose is the minimum angle of inclination of a plane with the horizontal in such a way that the body placed on it begins to slide down. It depends upon limiting friction.
- Further, when a body moves on an inclined plane then several forces work on it viz. normal reaction of plane, friction force acting in opposite direction of motion, gravitation force vertically down etc.
Pushing or pulling an object
- To pull an object (such as lawn mower) is always easier than to push whenever the force is applied at an angle to the object. This is because horizontal component of force will act to move the object. so:
- If we push, then the vertical component of force will press the object downward and the friction will be more.
- If we pull then the Vertical component of force will act upward and the friction will be less.
Speed, Time & Distance – Introduction & Concept
- Speed Distance Time is one of the most popular and important topics in the Mathematics or Quants section of any competitive exam. The concept of Speed, Time and Distance is used extensively for questions relating to different topics such as motion in a straight line, circular motion, boats and streams, races, clocks, etc. Aspirants should try to understand the inter-relationship between the factors speed, distance and time.
- Relationship Between Speed, Time & Distance
- Speed = Distance/Time – This tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.
- Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,
- Distance = Speed X Time, and
- Time = Distance / Speed, as the speed increases the time taken will decrease and vice versa.
What is Angular Velocity?
Angular Velocity Definition
- Angular velocity is the vector measure of the rotation rate, which refers to how fast an object rotates or revolves relative to another point.
- In simple words, angular velocity is the time rate at which an object rotates or revolves about an axis. Angular velocity is represented by the Greek letter omega (ω, sometimes Ω). It is measured in angle per unit time; hence, the SI unit of angular velocity is radians per second. The dimensional formula of angular velocity is [M0 L0 T-1].
- For an object rotating about an axis, every point on the object has the same angular velocity. But points farther from the axis of rotation move at a different tangential velocity than points closer to the axis of rotation. Angular velocity is also known as rotational velocity and angular frequency vector.
Relation Between Torque And Speed
- Torque is the rotational equivalence of linear force. Speed measures the distance covered in unit time. The relation between torque and speed are inversely proportional to each other. The torque of a rotating object can be mathematically written as the ratio of power and angular velocity.
- Viscosity is another type of bulk property defined as a liquid's resistance to flow. When the intermolecular forces of attraction are strong within a liquid, there is a larger viscosity. An example of this phenomenon is imagining a race between two liquids down a windshield.
Torque and Speed Formula
Torque = Power/speed
T = p/w
P is the power (work done per unit time)
τ is the torque (rotational ability of a body)
ω is the angular speed/velocity (rate of change of angular displacement)
The above equation can be rearranged to compute the angular velocity required to achieve given torque and power. The torque injects power and it purely depends on instantaneous velocity.