VIDHYAKSHETHRA

Aristotle's Fallacy :  A fallacy is an argument that is not logically sound. The truth of the conclusions of an argument does not determine whether the argument is a fallacy - it is the argument which is fallacious. The Greek thinker Aristotle held the view that if a body is moving, some external force is required to keep it moving. This is called Aristotle's Fallacy. Aristotle coded practical experience in the form of a basic argument. He failed to consider the effect of friction on motion. If friction was absent, there would be no need of a constant external force to keep the body in uniform motion.To get the true law of nature for forces and motion, one has to imagine a world in which uniform motion is possible with no frictional forces opposing. This is what Galileo did. The Law of Inertia :  Galileo studied motion of objects on an inclined plane. Galileo concluded that an object moving on a frictionless horizontal plane must neither have acceleration nor retardati...

Uniform Circular Motion : When an object follows a circular path at a constant speed, the motion of the object is called uniform circular motion. The word “uniform” refers to the speed, which is uniform (constant) throughout the motion. Since the velocity of the object is changing continuously in direction, the object undergoes acceleration. The acceleration of an object in uniform circular motion is always directed towards the centre of the circle. Let r and r′ be the position vectors and v and v′ the velocities of the object when it is at point P and P′ as shown in Fig.(a). By definition, velocity at a point is along the tangent at that point in the direction of motion. The velocity vectors v and v′ are as shown in Fig.(a1). Δv is obtained in Fig.(a2) using the triangle law of vector addition. Since the path is circular, v is perpendicular to r and so is v′ to r′ . Therefore, Δv is perpendicular to Δr. Since average acceleration is along Δv, a = Δv/Δt, the average accel...

Projectile : An object that is in flight after being thrown or projected is called a projectile. A stone thrown into a pond is an example of a projectile. The motion of a projectile is the result of two separate, simultaneously occurring components of motions (vertical and horizontal). One component is along a horizontal direction without any acceleration and the other along the vertical direction with constant acceleration due to the force of gravity. It was Galileo who first stated this in-dependency of the horizontal and the vertical components of projectile motion in his Dialogue on the great world systems (1632) .  Velocity components of a projectile   After the object has been projected, the acceleration acting on it is that due to gravity which is directed vertically downward: a j = −g  Or, a x = 0, a y = – g The components of initial velocity v o are : v ox = v o cos θ o          v oy = v o sinθ o ...

Average Velocity : The average velocity is the ratio of displacement and corresponding time interval. The direction of velocity is same as that of displacement vector. i.e. the direction of velocity at any point on the path of an object is tangential to the path at that point and is in the direction of motion. Instantaneous Velocity : It is given by the limiting value of the average velocity as the time interval approaches zero or it is the velocity at any point on the motion path. Average Acceleration : The average acceleration of an object for a time interval moving in x-y plane is the change in velocity divided by the time interval.    Instantaneous Acceleration :  It is the limiting value of the average acceleration as the time interval approaches zero. Equations of motion for uniform acceleration : Motion in a plane (two-dimensions) can be treated as two separate simultaneous one-dimensional motions with constant acceleration ...