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Angular Motion

We know that each rotating body or object has an axis of rotation. In most of the cases this axis changes with time. Now let’s think about a fixed axis. Here each point of the rotating body moves in circle around the fixed axis of rotation. 

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This motion is called as angular motion. Angular Motion EquationsAngular displacement equation is given belowAngular displacement (??) = ?f – ?iAngular displacement given in terms of “Radian”. One Radian is the angle subtended by an arc at the center of the circle, where the length of the arc is equal to the radius of the circle.Hence 1 Radian = S/RHere,S = Arc of the circleR = Radius of the circle Angular velocity is defined as the time rate of change of the angular displacement. ? =??/?tWhere,?? = change in angle when the point is moving from one position P to other position Q.?t = change in time occurred for this angular displacement.

Angular velocity is also be defined as the frequency of revolutions.? = 2?fAngular acceleration is the time rate of change of the angular velocity.a = ? ?/?twhere,? ? = change in angular velocityAnd ?t = change in timeNow, ? ? = 2?fTherefore: a = 2?f/?tAngular Motion DefinitionAngular motion is defined as the motion of a body on a fixed axis or fixed point. Angular Projectile MotionAngular projectile motion means that the projectile is launched by making some initial angle with the horizontal. 

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Suppose the initial velocity, with which the projectile is launched, makes angle q with the horizontal direction.Equation for the range of Projectile motion can be given as:Range = (vcos?( (vsin? + ((vsin?)2 + 2gy0)1/2))/gWhere,Range = horizontal distance coveredT = angle at which projectile was initially launchedy0 = initial height of the projectilev0 = initial velocity of the projectileAngular Motion ExamplesProblem 1: Suppose the radius of the wheel of the cycle is 25 cm. 

Calculate the distance travelled by the cycle while covering 200 revolutions?Solution: As mentioned above angular displacement is expressed as the time rate of change of angle. Now here we need to calculate the distance travelled by the bicycle. Cycle wheel has made 200 revolutions.? = (200 rev) (2? rad)/ 1 rev? = 1256 (rad)Hence angular displacement is = 1256 x .25 = 314 mHence the cycle covers 314 meters during 200 revolutions.