Motion

Motion Motion Motion or movement is a topic and a concept which we experience every moment! There is not a second that we can claim that an object is not moving. It is fascinating to understand everything in the Universe is moving. But how? If we are sitting in our room by ourselves, we say that we are just sitting and not moving. But it should be noted that the person sitting in the room is simply sitting with respect to his roommate. But how about with respect to Moon? It may sound overwhelming, but yes because we are on Earth and Earth is continuously spinning around its own axis and around the axis of the Sun, if there is a person standing on the Moon, he will say that the person sitting in the room is also moving. So with the above example it is to be understood that the terms moving and not moving are relative terms, dependent on the surroundings. Whether we look at an apple falling from a tree, or the chemical and nuclear reactions, or the case of heart pumping blood, everything is moving and this change in position is termed as Motion. What is Motion? Motion is the change in an objects position with respect to its surroundings. Motion is also defined as the process of any movement or the action of being moved. The study of motion plays a huge and a very important role in Physics. The concepts of Physics always revolve around the aspect of motion. In Physics, the study of the motion of objects is termed as Mechanics. The branch of Mechanics which involves describing the motion of objects using various tools such as equations, diagrams and graphs is known as Kinematics. This motion is usually described in terms of distance, time, displacement, velocity and acceleration. Distance and Displacement: Distance is the physical quantity which describes how much path or ground an object has entirely covered during its motion. Distance is a scalar quantity as it only has magnitude and no direction. Displacement is the physical quantity which describes the objects overall change in position. It is also defined as the shortest distance of an object from its initial position to its final position. In many cases it is typically distinct from the objects actual path covered. Displacement is a vector quantity as it has both magnitude and direction. Let us look at an example below which tells us the difference between distance and displacement. Let a car starting at point P travel 3m down South and then 4m in the East direction as shown in the figure on the right. The cars initial position is at point P and its final position is at point B. The total distance travelled by the car = PA + PB = 3m + 4m = 5m However, the displacement of the car must be the shortest distance from the initial point to the final point, and this implies displacement = PB We can calculate PB by using Pythagorean Theorem == PB = (32 + 42) = 25 = 5m Hence the displacement of the same car is 5m. Speed and Velocity: The term used for describing how fast an object is moving is Speed. Speed is a scalar quantity as it is associated only with the magnitude. An object travelling faster has greater speed, and hence covers more distance in less amount of time. Velocity is a physical quantity which describes the rate at which an object changes its position from one point to another. Velocity is a vector quantity as magnitude and direction both apply to it. Acceleration: Acceleration is defined as the rate at which an object changes its velocity. This implies that an object is said to be accelerating only if it is changing its velocity. If the object is not changing its velocity and instead travels with a uniform velocity, then the acceleration of that object is said to be 0. If an object has an initial velocity of u and final velocity of v, then the average acceleration of that object in a certain time interval of t can be calculated using the formula shown below: Types of motion: There are 2 types of motion based on whether an object covers equal distances or unequal distance in a certain interval of time. a) Uniform motion: If an object covers equal amount of distances in equal intervals of time (it is alright if the time intervals are really short), then such a motion is known as the Uniform motion. Example: If a car covers 5m in the 1 second, 10m in 2 seconds, 15m in 3 seconds, then we say that the car is travelling with uniform motion as it is covering constant 5m in every single second. b) Non-Uniform Motion: If an object covers unequal amount of distances in equal intervals of time, or if it covers equal amount of distances in unequal intervals of time, then such a motion is known as the Non-uniform motion. Example: If a car initially travels 5m in the first second and then 12m in 2 seconds, and 18m in 3 seconds, and so on then it is non-uniform motion. Motion is primarily classified into 3 types based on the path taken by the object in motion: 1) Translatory motion: If the position of an object changes with respect to a fixed point (or object), without a change in its orientation, then such a motion is known as the Translatory motion. Theoretically the path of an object in pure translatory motion can be a linear path or a curved path. The motion along a straight line path is known as the linear motion and the motion along a curved path is known as the curvilinear motion. Examples: A bus moving on the road, path of a moving vehicle on a straight road. 2) Rotatory motion: If an object moves in a circular path about a fixed point in space (about the axis of rotation) is known as the Rotatory motion. Examples: The wheel of any moving vehicle, hands of a clock, spinning top etc. 3) Oscillatory motion: The to and fro motion of an object is known as the Oscillatory motion. Examples: Swinging pendulum, swings in a playground, swinging cradle etc. There are other types of motion such as vibrational motion, periodic motion, random motion which can also be observed in our daily life. Newtons Laws of Motion: Isaac Newton, a scientist in the 17th century put forward 3 laws that explain why the objects move and why they dont move. These 3 laws have been popularly known as the Newtons Laws of Motion. These laws are extremely important and are the baseline for various concepts in physics. 1)Newtons First Law of Motion: The first law states that an object at rest stays in rest and an object in motion continues to stay in motion (with the same speed in the same direction), unless acted upon by an unbalanced force. This law brings out an underlying concept known as the Inertia. Inertia can be defined as the tendency of an object to resist a change in its motion. Example: A coffee placed inside a car remains steady even when the car is moving forward. But in a situation when a sudden brake is applied, as the coffee continues going forward with the same speed in the same direction, it is spilled all over the wind shield. 2)Newtons Second Law of Motion: The second law states that the acceleration of an object as produced by a net force is inversely proportional to the mass of the object, and is directly proportional to the magnitude of the net force (direction being the same as the net force). This law when translated to a mathematical statement can be written as shown below: The above equation when rearranged gives us: 3)Newtons Third Law of Motion: When objects come in contact with each other, as a result of those interactions the push or pull that acts upon the objects is termed as Force. There are forces which are termed as Contact Forces as they result from interactions that come through contact. Examples of contact forces are normal force, tension force, frictional force, and any applied forces. There are other types of forces that show effect even from a distance. Examples of such forces are gravitational force, magnetic force, electrical force etc. According to Newton, whenever objects interact with each other they apply force on each other. And in this interaction the 2 forces that act upon the objects in contact, are the action-reaction forces. So Newtons third law states that, every action has an equal and opposite reaction. So this law clearly explains that forces always come in pairs, and when the objects are in contact with each other the size of forces (magnitude) on the first object by the second, and on the second object by the first are the same. The direction of force exerted on the first object is opposite to the direction of force exerted on the second object. Example: When a person sits on the chair, the person exerts downward force on the chair and the chair exerts upward force on the person. This is an action-reaction pair resulting from the contact between the person and the chair. Equations of Motion: There are 3 equations of motion which are used to describe motion of any object. These equations are in terms of distance, time, displacement, velocity and acceleration. 1)First Equation of Motion: Consider an object travelling on a straight line with an initial velocity of u at t = 0, and reaches final velocity in a certain time interval of t. If the acceleration during this time interval is a, then the first equation of motion is given as: Acceleration, a = Change in velocity/ Time a = (v u) / t This can also be written as == a * t = (v u) The above when rearranged gives us: v = u + a*t Example: A car initially starts at rest and when time is 6 seconds it travels with a velocity of 30m/s. What is the acceleration of the car in this time interval? Given: Car starts at rest == at t = 0, initial velocity, u = 0m/s After t = 6 seconds, final velocity, v = 30m/s Acceleration, a = ? From the first equation of motion we have: v = u + at This implies: 30 = 0 + a*6 == 30 = 6a == a = 30/6 = 5m/s2 Therefore, the acceleration of the car is 5m/s2 in the given time interval. 2)Second Equation of Motion: Let u = initial velocity of an object v = final velocity of an object t = total time taken for the object to travel a displacement = d a = acceleration of the object We know that: Average Velocity = Total displacement covered / Total time taken Now, Average Velocity can be written as the average of the initial velocity and the final velocity of an object. Therefore, average velocity = (u + v)/2. Substituting this average velocity in the above equation we get: (u + v)/2 = Total displacement covered / Total time taken ==(u + v)/2 = d/t. This gives: (u + v) = 2d/t Now from the First Equation of Motion we have: v = u + at. Substituting this into the above equation we get: (u + u + at) = 2d/t == 2u + at = 2d/t == t * (2u + at) = 2d == 2ut + at2 = 2d Now solving for d, we get: d = 1/2 * (2ut + at2) == d = ut + *at2 Example: Andrew is waiting at a stoplight. When the stoplight turns to green, Andrew accelerated from rest at a rate of 8.00 m/s2 for a time of 4 seconds. What is the displacement of Andrews car during this time period? Given: Initial velocity of the car, u = 0m/s Acceleration, a = 8m/s2 Time taken, t = 4seconds Displacement, d = ? From the given information, here we can use the Second Equation of Motion. Therefore, d = ut + * at2 == d = (0* 4) + (1/2 * 8 * 42) == d = 64m Hence the displacement of Andrews car during the given time period is 64m 3)Third Equation of Motion: Let u = initial velocity of an object v = final velocity of an object t = total time taken for the object to travel a displacement = d a = acceleration of the object From the First Equation of Motion we have: v = u + at. This equation when rearranged gives us (v- u) = at Equation 1 Now, we know that: Average Velocity = Total displacement covered / Total time taken (u + v)/2 = d/t. Hence (v + u) = 2d/ t Equation 2 Now multiplying both Equation 1 and Equation 2 we get: (v u) (v + u) = at * 2d/t Therefore we get: (v2 u2) = 2ad Example: Edward is driving a bike and he accelerates from 4m/s to a speed of 10m/s over a distance of 20m. What is the acceleration of the bike? Given: Initial velocity, u = 4m/s Final velocity, v = 10m/s Distance covered, d = 20m Acceleration, a = ? From the given information, here we can use the Third Equation of Motion. Therefore, v2 u2 = 2ad == (102 42) = 2* a* 20 == (100 16) = 40 * a == 84 = 40 * a Now solving for a we get: a = 84/40 == a = 2.1m/s2