Uniform Circular MotionUniform circular motion is the motion of an object in a circle at a constant speed or velocity. An object moving in a circle is changing its direction continuously. An object moving in a circle is said to be moving in tangent of the circle. Since for this object, direction of its velocity vector is same as that of object’s motion. The velocity vector of the moving object is also present at tangential position of the circle.
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Angular Velocity FormulaAngular velocity is defined as the ratio of angular displacement and time taken to traverse this angle. It is expressed asω =∆θ/∆twhere,∆θ= 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 can also be defined as the frequency of revolutions.ω = 2∏f
Uniform MotionAn object moving in a straight line with constant speed is said to be in uniform motion. As we know that motion is defined as change in position of an object with respect to a point or other object. Suppose an object A is moving with respect to object B. In case of uniform motion of object A, there is no applied force on object A from view of B. Hence from the object B, A is neither accelerating nor decelerating. Hence A is in uniform motion.
Formula for Angular VelocityAngular velocity is the ratio of angular displacement to time rate. The formula for angular velocity is given asω =∆θ/∆t
Uniform Motion ProblemsThe uniform motion problems are of various types but most of them involves the following equation: d="r.t"Whered = distance;r = rate of object;t = time.
Ex. Two people are running on same track with following parameter:First RunnerSecond RunnerRater + 0.4rTime225 seconds240 secondsFind the distance travelled and rate of runners?Ans.Distance Travelled by first runner = 225 (r + 0.4);Distance Travelled by second runner = 240 r;Since both travel same distance so both the distance should be equated;225r + 90 = 240r;15r = 90;r = 6;The rate of slow runner is 6 m/sec and fast runner is 6.4. The distance travelled by both of them is 1440 m.
What is Uniform Motion?An object is said to be in uniform motion if it is moving in a straight line with constant speed. It is neither changing its directions nor is it moving in a curve. There is no change in its speed i.e. no acceleration or deceleration.
Uniform Circular Motion ProblemsThe uniform circular motion problems are of various types but they involve circular motion equation like;ω = 2π / T radians/sec;whereω = angular velocity;T = TimeEx. A runner runs on a circular track in time T = 10 sec. Find the angular velocity?Ans.ω = 2π / 10;ω = 0.628 radians/sec