Understanding Motion through Experience Class 9 Notes Advanced Science Chapter 2
Reviewing Class 9 Advanced Science Notes and Chapter 2 Understanding Motion through Experience Class 9 Notes regularly helps in retaining important facts. Understanding Motion through Experience Notes Class 9 Advanced Science Class 9 Understanding Motion through Experience Notes Motion Motion is a fundamental concept that we observe in everyday life. There are three branches of […]
ReviewingClass 9 Advanced Science Notesand Chapter 2 Understanding Motion through Experience Class 9 Notes regularly helps in retaining important facts. Class 9 Understanding Motion through Experience NotesMotionMotion is a fundamental concept that we observe in everyday life. There are three branches of mechanics that examine the motion of an object such asStatics: It is a branch of mechanics in which we study the objects at rest. In statics, time factor does not play any role. Kinematics: It describes the motion of objects without looking at the cause of the motion. Here, time factor plays an important role. Dynamics: It relates the motion of objects to the forces which cause them. The time factor also plays an important role. Frame of Reference:To describe the state of motion of an object, we must first specify a reference point. Without a reference point, it is impossible to say whether an object is moving or at rest. We choose a rectangular coordinate system of three mutually perpendicular axes as x, y and z. The point of intersection of these three axes is called origin (O) and is considered as the reference point. The x, y, z-coordinates describe the position of the object w. r. t. the coordinate system. To measure time, we need a clock. This coordinate system alongwith a clock constitutes a frame of reference. So, the frame of reference is a coordinate system with a clock, w. r. t. which an observer can describe the position, displacement, acceleration of an object. → Types of Frames Reference:(i) Inertial Frame of Reference:A frame that is at rest or moves with a constant velocity (uniform motion in a straight line) is called an inertial frame. In such frames, Newton’s laws of motion hold without any modification. For example, a train moving with constant speed on a straight track, or a laboratory fixed on the ground, can be considered an approximately inertial frame. (ii) Non-Inertial Frame of Reference:A frame that is accelerating (speeding up, slowing down, or changing direction) is called a non-inertial frame. In non-inertial frames, Newton’s laws do not hold directly, and we must introduce fictitious forces, also known as pseudo forces, to explain the observed motion. Example – Pseudo Force in a BusWhen a stationary bus suddenly starts moving forward, a passenger standing inside feels pushed backward. This apparent backward push is a consequence of the non-inertial (accelerating) nature of the bus frame. To describe the passenger’s motion from inside the bus, a pseudo force acting in the backward direction must be introduced. → Rest:If the position of an object does not change w. r. t. its surrounding with the passage of time, the object is said to be at rest. e. g. Book lying on the table, a person sitting on a chair is at rest with respect to surroundings etc. → Motion:If the position of an object is continuously changing w. r. t. its surroundings, then it is said to be in the state of motion. Thus, motion can be defined as a change in position of an object with time. Motion can be slow or fast, straight or curved (rectilinear or curvilinear) and uniform and non-uniform. Motion and rest are relative terms because an object’s state depends on the observer’s frame of reference not an absolute standard. An object can be in motion relative to one observer while being at rest relative to another at the same time. → Illustration – Motion is RelativeConsider two students walking side-by-side at the same speed in the same direction along a corridor. With respect to each other, their relative velocity is zero and each appears to be at rest. However, with respect to the classroom walls, both are clearly in motion. This demonstrates that motion has no absolute meaning; it can be defined only after specifying a frame of reference. Uniform and Non-Uniform Motion→ Uniform Motion:A body is said to be in uniform motion if it travels equal distances in equal intervals of time. The distance travelled by an object in uniform motion increases linearly. e. g. A car moving along a straight-line path covers equal distances in equal intervals of time, it is said to be in uniform motion. → Non-Uniform Motion:A body is said to be in non-uniform motion if it travels unequal distances in equal intervals of time. e. g. A car moving through a crowded market has non-uniform motion. Scalars and VectorsTo describe the motion of an object to be in two-dimensions or three-dimensions, we need to understand the concept of vectors first. Physical quantities that possess both magnitude and direction need a special mathematical language i. e. the language of vectors. On the basis of magnitude and direction, all the physical quantities are classified into two groups as scalars and vectors. → Scalar Quantities:These are the physical quantities that have only magnitude but no direction. It is specified completely by a single number with an appropriate unit. e. g. Temperature, distance, mass, length, time, work, etc. → Vector Quantities:These are the physical quantities that have both magnitudes and directions and obey the triangle/parallelogram laws of addition and subtraction, e. g. Displacement, acceleration, velocity, momentum, force, etc. A vector is represented by a boldface type or by an arrow placed over a letteri. e. F, a, b or \(\vec{F}\), \(\vec{a}\), \(\vec{b}\)Note:The magnitude of a vector is often called its absolute value, indicated by | v | = v. e. g. Suppose a body has a velocity 40 m/s due East. If 1 cm is chosen to represent a velocity of 10 m/s, a line OP of 4 cm in length and drawn towards East with an arrowhead at P will completely represent the velocity of the body. The point P is called head or terminal point and point O is called tail or initial point of the vector OP. The length of the line gives the magnitude and the arrowhead gives the direction. Distance versus DisplacementDistance is the total path length travelled by a body and is a scalar quantity. Displacement is the shortest straight-line distance between the initial and final positions of the body, together with its direction, and is a vector quantity. Example: A student walks 5 m from point A to point B along a straight line and then walks back from B to A. The total distance covered is 5 + 5 = 10 m, whereas the net displacement is zero, since the final position coincides with the initial position. This shows clearly that distance depends on the path taken, while displacement depends only on the initial and final positions. Addition of Vectors (Graphical Method)When two or more vectors act on a body simultaneously, their combined effect is represented by a single vector called the resultant. The process of combining vectors is known as vector addition. Two vectors can be added only if both of them are of same nature e. g. , a displacement vector cannot be added to a force but can be added to another displacement vector. Graphical method of addition of vectors helps us in visualising the vectors and the resultant vectors. This method contains following laws→ Triangle Law of Vector Addition:This law states that if two vectors can be represented both in magnitude and direction by the two sides of a triangle taken in the same order, then their resultant is represented completely, both in magnitude and direction, by the third side of the triangle taken in the opposite order. Consider two vectors A and B that lie in a plane as shown in Fig. (a). From a common point O, draw a vector OM equal and parallel to vector A as shown in Fig. (b). From head of OM, draw a vector MN equal and parallel to vector B. Then, the resultant vector is given by ON which joins the tail of A and head of B. The resultant of A and B is ON = OM + MNorResultant vector, R = A + B. → Parallelogram Law of Vector Addition:This law states that if two vectors acting on a particle at the same time are represented in magnitude and direction by two adjacent sides of a parallelogram drawn from a point, then their resultant vector is represented in magnitude and direction both by the diagonal of the parallelogram drawn from the same point. Consider two vectors A and B that lie in a plane as shown in Fig. (a). From a common point O, draw a vector OP equal and parallel to A arid vector OR equal and parallel to B. Complete the parallelogram OPQR as shown in Fig. (b). Then, the resultant vector is given by OQAccording to parallelogram law of vector addition,OQ = OP + ORResultant vector, R = A +BVector Subtraction (Graphical Method)To subtract vector B from vector A, we first reverse the direction of B to obtain – B. The subtraction of B from A is the same as the addition of B to A. A – B = A + (- B)The resultant A + (- B) is then obtained using the triangle law or the parallelogram law, as explained above. → Kinematic Equations for Uniformly Accelerated Motion:If the change in velocity of an object in each unit of time is constant, then object is said to be moving with constant acceleration and such a motion is called uniformly accelerated motion. (i) Velocity-time relation, v = u + at(ii) Position-time relation, s = ut – ½ at2(iii) Position-velocity relation, v2= u2+ 2as→ Displacement of the Particle in nth Second:Let an object is moving with initial velocity u under constant acceleration a. From the second equation of motion,s = ut + ½ at2where,t = time,s = displacement in time tDistance travelled in n seconds,sn= un + ½ an2To find the displacement in nth second, we subtract the position of particle at (n – 1)th second from the position of the particle at nth second. Distance travelled in the nth second = sn– sn-1snth= [un + ½ a(n2)] – [u (n-1) + ½ a (n-1)2]= un + ½ an2– un + u – ½ a (n – 1)2= u + \(\frac{a}{2}\) [n2– (n – 1)2]= u + \(\frac{a}{2}\) (n2– n2– 1 + 2n)= u + \(\frac{a}{2}\) (2n – 1)Displacement in the nth second, s (nth) = u + \(\frac{a}{2}\) (2n – 1)