Representation of a vector by coordinates: Let us consider OX, OY and OZ are three perpendicular axes, where O is the origin. Let P is a point with coordinates (x, y, z) and  =  is the position vector of P. , and are the unit vectors along + ve X, Y and Z axis. Let […]
Resolution of a vector into its components is the process to determining a set of vectors, whose resultant is the given vector. Each vector in that set is called a component of the given vector. Prove: Let us consider (= ) is resolute along the line OA and OB creates angles  and  with OC respectively.
Triangle law of vector addition: Statement: If two vectors are represented both in magnitude and direction by two sides of a triangle taken in the same order, then the resultant of these vectors is represented both in magnitude and direction by the third side of the triangle taken in the opposite order. Prove: Let us
Scalar: The quantities which are represented by magnitude and no directions and follow the ordinary algebra are called scalar quantity. Example: mass, volume, speed, density etc. Vector: The quantities which are represented by magnitude and directions and follow a special type of algebra (vector algebra) are called vector quantity. Example: velocity, acceleration, force etc. Representation
Bending of a cycle: When a cyclist moves on a curved road of radius r with sped v, he bends slightly at angle θ from his vertical position towards the inner side of the curve. m is the combined mass of the cycle and cyclist. The reaction force (R) offered by the road makes angle
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4. A liquid is kept in a cylindrical vessel of radius r which is rotated about its axis with angular speed . Find the difference in the height of the liquid at the centre of the vessel and its side. We consider a point mass m at point P (x, y) on the surface of
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1. A conical funnel rotates about its own axis with angular speed . A particle remain stationary on the inner surface of the funnel and it describes a horizontal circular motion of radius r as shown in figure. The coefficient of friction between particle and inner surface of the funnel is . What is the
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Circular motion of a body in vertical plane:Â A body of mass m is moving in a circular path of radius r in a vertical plane using an inextensible massless string. The velocity of the body at highest point (point P) is v1 and velocity at lowest point (point Q) of its motion is v2.
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The basic information of angular displacement, angular velocity and angular acceleration is given in Free Course-Class IX-Motion. To get this click the button. Click here Unit vectors along the radius and tangent: Let us consider OX and OY are two mutual perpendicular axes and O is the origin. A particle is moving in a circular
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Defects of vision of human eye: The most distant point which an eye can see clearly is called the far point (F). For the normal eye the far point lies at infinity. The nearest point which an eye can see clearly is called the near point (N). For normal eye, near point lies at a
