File Name: physics tips and tricks .zip
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Mechanics Vectors o o o o o o 1. A1 A2 A A n , then the adjacent vectors can be inclined to 2S each other at angle. If any two vectors are parallel or equal, then the scalar triple product is zero.
While finding the angle between two vectors one should check that the two vectors are directed towards the point or away from point.
For resultant of two vectors of equal magnitude. T Magnitude of resultant q 3a. Significant figures and error analysis 1. The limit of accuracy of a measuring instrument is equal to the least count of the instrument. When a quantity is squared, the number of significant digits is not squared. Algebraic operations with significant figures General rule- Final result shall have significant figure corresponding to the number of significant digits in the least accurate variable.
Then in the sum or difference also, the number of significant digits after the decimal should be n. Example: 1. Hence, the result will be 8. Example: Then in the product or quotient, the number of significant digits should also be n. Example: 2. Hence the result when rounded off to two significant digits become Therefore the answer is When two quantities are multiplied, the maximum relative error in the result is the sum of maximum relative errors in those two quantities.
When we are considering result involving quotient of two quantities, the maximum relative error in the result is the sum of maximum relative errors in those quantities. If a body is dropped from the Aeroplane moving with horizontal velocity, then the body will also have horizontal velocity because of the horizontal velocity of the Aeroplane and problem reduces to body projected from height H with horizontal velocity.
In case of throwing a particle in a moving train. The particle has horizontal velocity because of the motion of the train and particle will have projectile motion. If one is interested in motion respect to the train, then it will not be projectile motion [observer is in ground frame].
Projectile motion on inclined plane- Range of the projectile on the inclined plane. When tan D 2 tan E particle strikes the plane horizontally. Relative Velocity 1. Identify the observed body and two observers.
If a body is in equilibrium, then it does not mean that no force acts on the body but it simply means that the net force resultant of any number of forces acting on the body is zero. Mass of a body is a measure of the resistance offered by the body to the change in velocity of the body. In other words, it is a measure of inertia of the body. Whenever a body loses a contact with the surface, the normal force becomes zero. In problems where a body loses contact, this concept should be used.
Area under the force time graph gives magnitude of impulse of the given force in given time. If the maximum force of friction is greater than the applied force, then the force of friction will be equal to the applied force. Acceleration of a body sliding down an inclined plane-. Tension 1. Tension force always pulls a body. Tension across massless pulley or frictionless pulley remains constant. Application of Newtons law to circular motion tion type of problems 1.
Draw free body diagram. Identify the direction of acceleration 3. Write equation of motion. To find out the direction of normal force Normal force will perpendicular to the surface of the body. Example: What minimum velocity v must be given to the solid cylinder of radius r, so that continues its motion without a jump down the incline. Solution: In the given position, Let Z be angular velocity of the cylinder about the point O. Bodies, which move together, can be considered as one system.
If bodies have different motions, they should be considered as separate bodies. To find internal forces for bodies moving together, treat them as single system to find acceleration then to find internal forces consider one of the bodies as system.
A horizontal force of 18 N is applied on 2kg block such that both blocks move together calculate the value of contact force between the two blocks. When a massive body suffers one dimensional elastic collision with a stationary light body, the velocity of massive body remains practically unchanged but light body begins to move with a velocity which is double the velocity of massive body.
Momentum and total energy are conserved during elastic collisions. The coefficient of restitution gives you an idea of the degree to which kinetic energy is conserved. When kinetic energy is conserved one can either use kinetic energy equation or the coefficient of restitution formula. In the perfectly inelastic collision, the relative velocity of the bodies after the collision is zero. If a ball is dropped from a height h.
In head on collision also called as one dimension collision. Bodies move along same straight line before and after collision. Work, Power, Energy 1. For conservative forces work done along a closed path is Zero. For non conservative forces work done along a closed path is not equal to zero. Work done against friction depends on the path followed. Viscosity and friction are non-conservative forces.
Work done by electric force and gravitational force does not depends upon path followed. They are called as conservative forces. Work done depends on the frame of reference. Conservative laws can be used to describe the behavior as mechanical system even when the exact nature of forces is not known. Kinetic energy of a body cannot change if the force acting on a body is perpendicular to the instantaneous velocity.
In case of conservative force power is not dissipated , work does not depend upon the path followed. It depends upon initial and final position of the body In case of friction, power depends on the path followed.
When momentum increases by factor n kinetic energy increases by factor n2 if mass is constant. A body starting from rest moves along a smooth inclined plane of length A , height h and having angle of inclination T.
Centre of mass 1. Centre of mass coincides with the geometrical centre of the body for all symmetrical bodies with uniform distribution of mass. When a freely falling body explodes in to pieces the centre of mass as the whole system still lies on the same vertical line. For a shell moving on a parabolic path explodes in to pieces, the centre of mass of the system shall lie along the same parabolic path.
If centre of mass is chosen as the origin then some of moments of the masses of the system about the centre of mass is zero. Acceleration of centre of mass multiplied by total mass of the system gives total resultant force on the system. To find out centre of mass of combination of bodies 1. Find the system where whether it is one dimensional two dimensional or three dimensional.
If the system is one dimensional use length instead of mass 3. If the system is two dimensional use area instead of mass 4.
If the system is three dimensional use volume instead of mass 5. Locate the axis and locate the centre of mass of everybody. Use following formula to locate c. Some complex COM problems can be quickly and easily solved using concept of negative mass hypothetical concept.
Find the center of mass? Solution: Consider the system as. Use following formula to calculate velocity of c. For two dimension find X and Y component of velocity and for three dimension find X, Y and Z component of velocity 9. Do the same to find out acceleration. Gravitation 1. Hence, the following two equations are used in most of the cases. If masses of sun and planet are comparable and motion of sun is also to be considered, then both of them revolve around their centre of mass with same angular velocity but different angular velocities in the circles of different radii.
The centre of mass remains stationary. The orbital velocity of a satellite is independent of the mass of the satellite but depends upon the mass and radius of the planet around which the rotation is taking place. Trajectory of a body projected from point A in the direction AB with different initial velocities: Let a body be projected from point A with velocity v in the direction AB.
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Mechanics Vectors o o o o o o 1. A1 A2 A A n , then the adjacent vectors can be inclined to 2S each other at angle.
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