1st Year Physics Chapter 2 Notes

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• Basic concepts of vectors
• What are vectors and Scalars
• Rectangular coordinate system: Two reference lines drawn at right angles to each other as shown in Fig. 2.1 (a) are known as coordinate axes and their point of intersection is known as origin. This system of coordinate axes is called Cartesian or rectangular coordinate system.
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• One of the lines is named as x-axis, and the other the y- axis. Usually the x-axis is taken as the horizontal axis, with the positive direction to the right, and the y-axis as the vertical axis with the positive direction upward.
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• The direction of a vector in a plane is denoted by the angle which the representative line of the vector makes with positive x-axis in the anti-clock wise direction, as shown in Fig 2.1 (b). The point P shown in Fig 2.1 (b) has coordinates (a,b). This notation means that if we start at the origin, we can reach P by moving 'a' units along the positive x-axis and then 'b' units along the positive y-axis.
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• The direction of a vector in space requires another axis which is at right angle to both x and y axes, as shown in Fig 2.2 (a). The third axis is called z-axis.
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• The direction of a vector in space is specified by the three angles which the representative line of the vector makes with x, y and z axes respectively as shown in Fig 2.2 (b). The point P of a vector A is thus denoted by three coordinates (a, b, c).
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• Addition of vectors
• Resultant vectors: The resultant of a number of vectors of the same kind-force vectors for example, is that single vector which would have the same effect as all the original veotors taken together.
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• Vector Subtraction: The subtraction of a vector is equivalent to the addition of the same vector with its direction reversed. Thus, to subtract vector B from vector A, reverse the direction of B and add it to A, as shown in Fig. 2.3 (d). A-BA+(-B) where (-B) is negative vector of B.
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• Multiplication of a Vector by a Scalar: The product of a vector A and a number n > 0 is defined to be a new vector na having the same direction as A but a magnitude n times the magnitude of A as illustrated in Fig. 2.4. If the vector is multiplied by a negative number, then its direction is reversed.
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• In the event that n represents a scalar quantity, the product nA will correspond to a new physical quantity and the dimensions of the resulting vector will be the product of the dimensions of the two quantities which were multiplied together.
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• For example, when velocity is multiplied by scalar mass m, the product is a new vector quantity called momentum having the dimensions as those of mass and velocity.
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• Unit Vector: A unit vector in a given direction is a vector with magnitude one in that direction. It is used to represent the direction of a vector.
• Vector subtraction
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• multiplication of a vector by a scalar
• Unit vector
• Null vector
• Equal vectors
• Rectangular components of a vector
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• Determination of a vector from its rectangular components
• Position vector
• Vector addition by rectangular components
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• Product of two vectors
• Scalar product or Dot product
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• Vector product or cross-product
• Definition of torque with examples
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• Equilibrium of forces
• The first condition of equilibrium
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• Equilibrium of torques
• The second condition of equilibrium
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