Physics Notes for NEET Chapter 0 PDF

Vectors 1 y ˆj x k̂ î z 60 Fig. 0.1 E3 Chapter (7) Orthogonal unit vectors ˆi , ˆj and kˆ are called orthogonal unit vectors. These vectors must form a Right Handed Triad (It is a coordinate system such that when we Curl the fingers of right hand from x to y then we must get the direction of z alon...

Vectors 1 y ˆj x k̂ î z 60 Fig. 0.1 E3 Chapter (7) Orthogonal unit vectors ˆi , ˆj and kˆ are called orthogonal unit vectors. These vectors must form a Right Handed Triad (It is a coordinate system such that when we Curl the fingers of right hand from x to y then we must get the direction of z along thumb). The D YG U Physical quantities having magnitude, direction and obeying laws of vector algebra are called vectors. Example : Displacement, velocity, acceleration, momentum, force, impulse, weight, thrust, torque, angular momentum, angular velocity etc. If a physical quantity has magnitude and direction both, then it does not always imply that it is a vector. For it to be a vector the third condition of obeying laws of vector algebra has to be satisfied. Example : The physical quantity current has both magnitude and direction but is still a scalar as it disobeys the laws of vector algebra. Types of Vector (1) Equal vectors : Two vectors A and B are said to be equal when they have equal magnitudes and same direction. ˆi  x , ˆj  y , kˆ  z y x z  x  xˆi , y  yˆj , z  zkˆ (8) Polar vectors : These have starting point or point of application. Example displacement and force etc. (9) Axial Vectors : These represent rotational effects and are always along the axis of rotation in accordance with right hand screw rule. Angular velocity, torque and angular momentum, etc., are example of physical quantities of this type. Axial vector (2) Parallel vector : Two vectors A and B are said to be parallel when Vectors ID Introduction of Vector 0 Axis of rotation (i) Both have same direction. (ii) One vector is scalar (positive) non-zero multiple of another U vector. ST (3) Anti-parallel vectors : Two vectors A and B are said to be anti-parallel when (i) Both have opposite direction. (ii) One vector is scalar non-zero negative multiple of another vector. (4) Collinear vectors : When the vectors under consideration can share the same support or have a common support then the considered vectors are collinear. (5) Zero vector (0 ) : A vector having zero magnitude and arbitrary direction (not known to us) is a zero vector. (6) Unit vector : A vector divided by its magnitude is a unit vector. Unit ˆ (read as A cap or A hat). vector for A is A Anticlock wise rotation Axis of rotation Clock wise rotation Axial vector Fig. 0.2 (10) Coplanar vector : Three (or more) vectors are called coplanar vector if they lie in the same plane. Two (free) vectors are always coplanar. Triangle Law of Vector Addition of Two Vectors If two non zero vectors are represented by the two sides of a triangle taken in same order then B the resultant is given by the closing side of triangle in opposite R  AB order. i.e. R  A  B B  OB  OA  AB A O A ˆ. ˆ  A  A AA Since, A A Thus, we can say that unit vector gives us the direction. (1) Magnitude of resultant vector Fig. 0.3 2 Vectors sin  BN B (2) Direction AN  AN  B cos B In  ABN , cos  tan    BN  B sin CN B sin  ON A  B cos Polygon Law of Vector Addition In OBN , we have OB  ON  BN 2 2 If a number of non zero vectors are represented by the (n – 1) sides of an n-sided polygon then the resultant is given by the closing side or the n side of the polygon taken in opposite order. So, 2 B th B sin B  A O R  ABCD E  A OA  AB  BC  CD  DE  OE N 60 R B cos 2Fig. 0.4 D  R  ( A  B cos  )  (B sin ) 2 2  R 2  A 2  B 2 (cos 2   sin2  )  2 AB cos  E3 E  R 2  A 2  B 2  2 AB cos  C C E  R 2  A 2  B 2 cos 2   2 AB cos   B 2 sin2  D R  R A 2  B 2  2 AB cos B, then If R makes an angle  with A, then in OBN , tan   B sin A  B cos  Resultant of three non co- planar vectors can not be zero. Subtraction of vectors D YG BN BN  ON OA  AN Note  Resultant of three co-planar vectors may or may not be zero A 2  B 2  2 AB cos tan   A A :  Resultant two unequal vectors can not be zero. Fig.of0.6 O U | A  B|  B ID (2) Direction of resultant vectors : If  is angle between A and B Parallelogram Law of Vector Addition If two non zero vectors are represented by the two adjacent sides of a parallelogram then the resultant is given by the diagonal of the parallelogram passing through the point of intersection of the two vectors. (1) Magnitude Since, R 2  ON 2  CN 2 Since, A  B  A  ( B) and | A  B |  A 2  B 2  2 AB cos A 2  B 2  2 AB cos (180 o   )  | A  B|  Since, cos (180   )   cos  | A  B |  A 2  B 2  2 AB cos   R 2  (OA  AN )2  CN 2 U R sum  A  B  R 2  A 2  B 2  2 AB cos  R | R | | A  B |  B R  AB B sin   O B cos Special cases : R  A  B when  = 0 o R diff  A  ( B ) B sin tan 1  A  B cos o A 2  B 2 when  = 90 and tan  2  o A 180 –  N Fig. 0.5 R B 1 2 B A A R  A  B when  = 180  C B  B A 2  B 2  2 AB cos  ST  Fig. 0.7 B sin(180   ) A  B cos (180   ) Vectors But sin(180   )  sin and cos(180   )   cos  cos   Ry  cos   Rz  R B sin  tan  2  A  B cos Resolution of Vector Into Components Y Ry R …(i) But from figure R x  R cos  …(ii) and R y  R sin …(iii) R x2  R y2  R z2 When a point P have coordinate (x, y, z) When a particle moves from point (x , y , z ) to (x , y , 1 R  R x  R y  R z q or R  R x ˆi  R y ˆj  R z kˆ Y U 2 2 ID Rectangular Components of 3-D Vector Thus if there are two vectors A and B having angle  between them, then their scalar product written as A. B is defined as A. B  AB cos  (2) Properties : (i) It is always a scalar which is positive if angle between the vectors is acute (i.e., < 90°) and negative if angle between them is obtuse (i.e. 90°