FSc ICS Notes Physics XI Short Questions & Definitions Chapter 2 Vectors and Equilibrium 1st Year Physics Notes Online Taleem Ilm Hub
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Scalar quantity or Scalar: A physical quantity which is
completely specified by a number associated with a suitable unit without any mention of
direction in space.
Vector quantity or Vector: A physical quantity which requires both a magnitude in proper units and a direction for its complete description; Graphically it is represented by a straight line, length of which is equal to its magnitude and arrow-head shows its direction.
Coordinate: Suitable sets of numbers with which the positions of points are specified.
Cartesian coordinates (or Rectangular coordinates): Coordinates referred to three mutually perpendicular straight lines.
Addition of vectors (head-to-tail rule): Addition of vectors is obtained by drawing their representative lines in such a way that tail of first vector coincides with the head of the second vector and so on. Join tail of first vector with the head of last vector. This joining vector will represent the vector sum.
Resultant vector: The resultant of a number of similar vectors, is the single vector which would have the same effect as all the original vectors taken together.
Vector subtraction: The subtraction of a vector is equivalent to the addition of the same vector with its direction reversed.
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.
Unit vector: A vector in a given direction with magnitude one in that direction.
Null vector: It is a vector of zero magnitude and arbitrary direction.
Equal vectors: Two vectors A and B are said to be equal if they have the same magnitude and direction, regardless of the position of their initial points.
Components of a vector: A component of a vector is its effective value in a given direction.
Rectangular components (of a vector): Resolving of a vector into components along mutually perpendicular directions called rectangular components.
Position vector: The position vector r is a vector that describes the location of a particle with respect to the origin.
Acrobat: One who performs skilled or daring gymnastic feats.
Aisle: A passageway leading to the seats in a place of assembly.
Product of two vectors: There are two types of vector multiplications. The product of these two types is known as scalar product and vector product.
Scalar Product ( or Dot Product ): The Scalar or dot product of vectors A and B is the scalar quantity obtained by multiplying the product of the magnitudes of the vectors by the cosine of the angle between them. Mathematically,
A ⋅ B = A B
cos θ
Vector Product ( or Cross Product ): The vector product of two vectors (say) A and B is defined to be a vector such that:
its magnitude is A B sin θ , θ being the angle between A
and B
its direction is perpendicular to the plane of A and B
and can be determined by right-hand-rule. Mathematically,
A x B = A B sin θ n
Right-hand rule (in Vector Product): First place together the tails of the two vectors. Then rotate the vector that occurs first in the product into the second vector through the smaller of the two possible angles. Curl the fingers of the right hand along the direction of rotation. The direction of the thumb will represent direction of the vector product.
Commutative Law: For a binary operation ∗ ,
a ∗ b = b ∗ a
Example : a + b = b + a and a ⋅ b = b ⋅ a
Associative Law: For a binary operation ∗ ,
( a ∗ b ) ∗ c = a ∗ ( b ∗ c)
Example : ( a ⋅ b ) ⋅ c = a ⋅ ( b ⋅ c ) and ( a + b ) + c = a + ( b + c )
Distributive law: For two binary operations ∗ and o . The operation ∗ is said to be distributive over the operation o , if
a ∗ ( b o c )
= ( a ∗ b ) o ( a ∗ c )
Example : a⋅( b +
c ) = ( a ⋅ b ) + ( a ⋅ c ) & a + ( b ⋅ c ) ≠ ( a
+ b ) ⋅ ( a + c )
Spanner: A wrench for tightening or loosening nuts.
Nut: A metal piece having an internal screw thread, as for securing or adjusting a bolt.
Torque (or Moment of force): The physical quantity which produces angular acceleration. Product of the force and its moment arm.
Moment arm: Perpendicular distance from the axis of rotation to the line of action of force.
Concurrent forces: Forces acting together on a body.
Angular velocity (ω): The rate of change of angular displacement.
Angular acceleration (α): The rate of change of angular velocity.
Coplanar forces: Forces in a single plane.
Equilibrium: State of balance in which the sum of all the forces and the sum of all the moments are equal to zero. If a body remains at rest or moves with uniform velocity, it is said to be in equilibrium.
Static equilibrium: State of rest.
Dynamic equilibrium: The state of a body moving with a uniform velocity or rotating with a uniform angular velocity.
Translational equilibrium: A body will be in translational equilibrium if and only if the vector sum of external forces acting on a body equal to zero.
Rotational equilibrium: An object is in rotational equilibrium if and only if the vector sum of external torque about any axis acting on it equals to zero.
Rigid body: A body is said to be rigid, if it is not possible to change its shape by the application of a force, however large.
Equilibrium of forces: If a body, under the action of a number of forces, is at rest or moving with uniform velocity, it is said to be in equilibrium.
First condition of equilibrium: Sum of all the force acting on a body along x-axis and along y-axis should be equal to zero. Mathematically Fx = 0 and Fy = 0
Second condition of equilibrium: The algebraic sum of all the torques acting on the body should be zero. Mathematically: Σ τ = 0
Astride: With the legs wide apart.
Polygon: A closed figure having many side and angles.
Rotation: Turning around its own axis or centre.
Configuration: Structured arrangement; figure; the spatial arrangement of atoms in a molecule or nucleons and electrons in an atom.
Span: The distance between two definite ends.
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