{"id":46757,"date":"2024-02-17T05:03:53","date_gmt":"2024-02-16T23:33:53","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=46757"},"modified":"2024-02-17T14:42:01","modified_gmt":"2024-02-17T09:12:01","slug":"plus-one-physics-notes-chapter-4","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-one-physics-notes-chapter-4\/","title":{"rendered":"Plus One Physics Notes Chapter 4 Motion in a Plane"},"content":{"rendered":"

Kerala Plus One Physics Notes Chapter 4 Motion in a Plane<\/h2>\n

Summary<\/span>
\nIntroduction<\/span>
\nIn this chapter, we will study, about vector, its \u2019 addition, substraction and multiplication We then discuss motion of an object in a plane. We shall also discuss uniform circular motion in detail.<\/p>\n

Scalars And Vectors<\/span><\/p>\n

a. Scalars:
\nA quantity which has only magnitude and no direction is called a scalar quantity.
\nEg: length; volume, mass, time, work etc.<\/p>\n

b. Vectors:
\n(i) The need for vectors:
\nIn one dimensional motion, there are only two possible directions. But in two or three dimensional motion, infinite number of directions are possible. Hence quantities like displacement, velocity, force etc. cannot be represented by magnitude alone: Therefore in order to describe such quantities, not only magnitude but direction also is essential.<\/p>\n

(ii) Vector:
\nA physical quantity which has both magnitude and direction is called a vector quantity.
\nEg: Displacement, Velocity, Acceleration, Force, momentum.<\/p>\n

1. Position and Displacement Vectors:
\nPosition vector:
\nConsider the motion of an object in a plane. Let P be the position of object at time tw.r.t.origin given O.
\n\"Plus
\nA vector representing the position of an object P with respect to an origin O is called position vector \\(\\overrightarrow{\\mathrm{OP}}\\) of the object. This position vector may be represented
\nby an arrow with tail at O and head at P.<\/p>\n

The length of the line gives the magnitude of the vector and arrow head (tip) indicates its direction in space. The magnitude of OP is represented by |\\(\\overrightarrow{\\mathrm{OP}}\\)|.<\/p>\n

Displacement vector:
\n\"Plus
\nConsider the motion of an object in a plane. Let P be the position of a moving object at a time t and p1<\/sup> that at a later time t1<\/sup>. \\(\\overrightarrow{\\mathrm{OP}}\\) and \\(\\overrightarrow{\\mathrm{OP}^{1}}\\) are the position vectors at time t and t1<\/sup> respectively. So the vector \\(\\overrightarrow{\\mathrm{PP}^{1}}\\) is called displacement vector corresponding to the motion in the time interval (t – t1<\/sup>).<\/p>\n

2. Equality of vectors:
\nTwo vectors are said to be equal if they have the same magnitude and direction.
\n\"Plus
\nThe above figure shows two vectors \\(\\vec{A}\\) and \\(\\vec{B}\\) having the same magnitude and direction.
\n\u2234 \\(\\vec{A}\\) = \\(\\vec{B}\\).<\/p>\n

Question 1.
\nObserve the following figures (a) and (b) and find which pair does represents equal vectors?
\n\"Plus
\nAnswer:
\nFigure a represent that A and B are equal vectors. Two vectors A1<\/sup> and B1<\/sup> are unequal, because they were in different directions.<\/p>\n

Multiplication Of Vectors By Real Numbers<\/span>
\nMultiplying a vector \\(\\vec{A}\\) with a positive number I gives a vector whose magnitude is changed by the factor \u03bb.
\n\"Plus
\nThe direction \u03bb\\(\\vec{A}\\) is the same as that of \\(\\vec{A}\\).
\nExamples:
\n\"Plus
\nA vector \\(\\vec{A}\\) and the resultant vector after multiplying \\(\\vec{A}\\) by a positive number 2.
\n\"Plus
\nA vector A and resultant vector after multiplying it by a negative number-1 and -1.5.<\/p>\n

Addition And Subtraction Of Vectors – Graphical Method<\/span>
\nVectors representing physical quantities of the same dimensions<\/u> can be added or subtracted. The sum of two or more vectors is known as their resultant.<\/p>\n

1. When two vectors are acting in the same direction:
\n\"Plus<\/p>\n

2. When two vectors act in opposite direction:
\nIn this case, the angle between the vectors is 180\u00b0.
\n\"Plus
\nThe resultant of the two vectors is a new vector whose magnitude is the difference between the magnitudes of the two vectors and whose direction is the same as the direction of the bigger vector.<\/p>\n

3. When two vectors are inclined to each other:
\nThe sum of two vectors inclined at an angle q can be obtained either by<\/p>\n