DYNAMICS Dynamics is a branch of physics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion. 2 Categories of Dynamics: 1. Linear Dynamics pertains to objects moving in a line and involves such quantities as force, mass/inertia, displacement (in units of distance), velocity (distance per unit time), acceleration (distance per unit of time squared) and momentum (mass times unit of velocity). 2. Rotational Dynamics pertains to objects that are rotating or moving in a curved path and involves such quantities as torque, moment of inertia/rotational inertia, angular displacement (in radians or less often, degrees), angular velocity (radians per unit time), angular acceleration (radians per unit of time squared) and angular momentum (moment of inertia times unit of angular velocity). Very often, objects exhibit linear and rotational motion. Where u is initial velocity in m/s, v is final velocity in m/s, s is the distance traveled in m, a is the acceleration in m/s2, t is the time taken in s. Solved Examples 1: John throws a ball and it moves along horizontal direction. If it travels a distance of 30 m in 2s. Calculate its acceleration. Solution: Given: Initial velocity u = 0, Distance traveled s = 30 m, Time taken t = 2 s Distance traveled is given by s = ut + 12 at2 30 = 0 + 12 a (2)2 30 = 2 a ∴ Acceleration a = 15 m/s2. 2: A train is moving on a straight line with a velocity of 40 km/hr is brought to rest by applying brakes after traveling a distance of 100 m. Calculate its retardation? Solution: Given: Initial velocity u = 40 km/hr = 40×10003600 = 11.11 m/s, Final velocity v = 0, Distance traveled s = 100 m, Using the formula v2 = u2 + 2as Acceleration a = v2−u22s = 0−(11.11)22×100 = 123.44200 = 0.617 m/s2. Newtons laws of motion Newton described force as the ability to cause a mass to accelerate. His three laws can be summarized as follows: First law: If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.[3][4] Second law: The rate of change of linear momentum P of an object is equal to the net force Fnet, i.e., dP/dt = Fnet. Third law: When a first body exerts a force F1 on a second body, the second body simultaneously exerts a force F2 = −F1 on the first body. This means that F1 and F2 are equal in magnitude and opposite in direction. Newtons Laws of Motion are valid only in an inertial frame of reference
Posted on: Tue, 09 Sep 2014 06:35:59 +0000
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