Physics CBSE Notes class 11, Study notes of Physics

Download Physics CBSE Notes class 11 and more Study notes Physics in PDF only on Docsity! 1 | P a g e www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) Physics Notes Class 11 CHAPTER 4 MOTION IN A PLANE part 1 Those physical quantities which require magnitude as well as direction for their complete representation and follows vector laws are called vectors. Vector can be divided into two types 1. Polar Vectors These are those vectors which have a starting point or a point of application as a displacement, force etc. 2. Axial Vectors These are those vectors which represent rotational effect and act along the axis of rotation in accordance with right hand screw rule as angular velocity, torque, angular momentum etc. Scalars Those physical quantities which require only magnitude but no direction for their complete representation, are called scalars. Distance, speed, work, mass, density, etc are the examples of scalars. Scalars can be added, subtracted, multiplied or divided by simple algebraic laws. Tensors Tensors are those physical quantities which have different values in different directions at the same point. Moment of inertia, radius of gyration, modulus of elasticity, pressure, stress, conductivity, resistivity, refractive index, wave velocity and density, etc are the examples of tensors. Magnitude of tensor is not unique. Different Types of Vectors (i) Equal Vectors Two vectors of equal magnitude, in same direction are called equal vectors. 2 | P a g e www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) (ii) Negative Vectors Two vectors of equal magnitude but in opposite directions are called negative vectors. (iii) Zero Vector or Null Vector A vector whose magnitude is zero is known as a zero or null vector. Its direction is not defined. It is denoted by 0. Velocity of a stationary object, acceleration of an object moving with uniform velocity and resultant of two equal and opposite vectors are the examples of null vector. (iv) Unit Vector A vector having unit magnitude is called a unit vector. A unit vector in the direction of vector A is given by  = A / A A unit vector is unitless and dimensionless vector and represents direction only. (v) Orthogonal Unit Vectors The unit vectors along the direction of orthogonal axis, i.e., X – axis, Y – axis and Z – axis are called orthogonal unit vectors. They are represented by (vi) Co-initial Vectors Vectors having a common initial point, are called co-initial vectors. (vii) Collinear Vectors Vectors having equal or unequal magnitudes but acting along the same or Ab parallel lines are called collinear vectors. (viii) Coplanar Vectors Vectors acting in the same plane are called coplanar vectors. 5 | P a g e www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) Magnitude of vector A = √Ax 2 + Ay 2 tan θ = Ay / Ax Direction Cosines of a Vector If any vector A subtend angles α, β and γ with x – axis, y – axis and z – axis respectively and its components along these axes are Ax, Ay and Az, then cos α= Ax / A, cos β = Ay / A, cos γ = Az / A and cos2 α + cos2 β + cos2 γ = 1 Subtraction of Vectors Subtraction of a vector B from a vector A is defined as the addition of vector -B (negative of vector B) to vector A Thus, A – B = A + (-B) Multiplication of a Vector 1. By a Real Number When a vector A is multiplied by a real number n, then its magnitude becomes n times but direction and unit remains unchanged. 2. By a Scalar When a vector A is multiplied by a scalar S, then its magnitude becomes S times, and unit is the product of units of A and S but direction remains same as that of vector A. Scalar or Dot Product of Two Vectors The scalar product of two vectors is equal to the product of their magnitudes and the cosine of the smaller angle between them. It is denoted by . (dot). A * B = AB cos θ 6 | P a g e www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) The scalar or dot product of two vectors is a scalar. Properties of Scalar Product (i) Scalar product is commutative, i.e., A * B= B * A (ii) Scalar product is distributive, i.e., A * (B + C) = A * B + A * C (iii) Scalar product of two perpendicular vectors is zero. A * B = AB cos 90° = O (iv) Scalar product of two parallel vectors is equal to the product of their magnitudes, i.e., A * B = AB cos 0° = AB (v) Scalar product of a vector with itself is equal to the square of its magnitude, i.e., A * A = AA cos 0° = A2 (vi) Scalar product of orthogonal unit vectors and (vii) Scalar product in cartesian coordinates = AxBx + AyBy + AzBz Vector or Cross Product of Two Vectors The vector product of two vectors is equal to the product of their magnitudes and the sine of the smaller angle between them. It is denoted by * (cross). 7 | P a g e www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) A * B = AB sin θ n The direction of unit vector n can be obtained from right hand thumb rule. If fingers of right hand are curled from A to B through smaller angle between them, then thumb will represent the direction of vector (A * B). The vector or cross product of two vectors is also a vector. Properties of Vector Product (i) Vector product is not commutative, i.e., A * B ≠ B * A [∴ (A * B) = — (B * A)] (ii) Vector product is distributive, i.e., A * (B + C) = A * B + A * C (iii) Vector product of two parallel vectors is zero, i.e., A * B = AB sin O° = 0 (iv) Vector product of any vector with itself is zero. A * A = AA sin O° = 0 (v) Vector product of orthogonal unit vectors (vi) Vector product in cartesian coordinates