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PHYSICS for NEET and JEE Pradeep Kshetrapal Class XI Portion
Chapter 4- Motion in a Plane Acceleration in Circular motion Phy-XI-4-11
An object is making circular motion. After time t it makes an angle with the horizontal ' dt dv t V Let the angular velocity be and linear velocity be v at this timet.
Let the angular velocity increases by dw and suppose it becomes o' during a very small interval of time dt. This change is dw. dt dv de Then we define angular acceleration as rate of change in angular velocity. change in angular velocity dao OC= time. dt.
Angular acceleration is a vector quantity. it has magnitude as well as direction Its unit is Rad/s2.Its direction is taken perpendicular to the plane of rotation as per right hand curl rule
Relation with Linear acceleration Let the change in linear velocity be dv Angular acceleration 0C C V dt dv t V dt dt'r 1 dv r dt Where a is linear acceleration of the point along velocity at circumference, r is radius
So, angular acceleration A- where, a is linear acceleration. ' dt dv t V Displacement x-R. a R.A
Two points on a single radius move in such a way that they form concentric circles as shown in figure: Here time period of the two body is same, T.
Similarities: T is same v is same is same But Now linear Velocity V - rw So linear velocity is different even if angular velocity is same Farther the point from centre, larger is its speed
Kinematic equation: Let us suppose a regulator of a fan is operated, the angular velocity changes from to and the time taken for such change is t. Let the angle made in time t is C V' dt dv t V dt so, oot At. This equation is similar to v-u+at.
Let the angular displacement at time t be . 1 2 (From second kinematic equation S-ut+ at). Now, the third kinematic equation for linear motion is 2as-v2- u2 So, in circular motion 2
If the acceleration is in the direction opposite to the direction of initial velocity then the velocity will decrease. U a If we apply the acceleration in the direction 90 to the direction of velocity then it will change the direction of motion. V- V +- t v-0+ at at Resultant velocity v
And so on it will form a circle. If we do apply the acceleration at every small instant of time then we get the path made by the body as a circle.
Av indicates change in velocity i.e., centripetal acceleration In a uniform circular motion, there is a uniform (constant) speed, but velocity changes. Suppose there is a velocity v1 acting at certain time in a circular motion. after time At. Let the velocity becomes v2 Acceleration -v1 , At
dx At centre When radius r turn by o small angle d At the circumference where velocity change the vector triangle is here' arc radius r arc do- radius locity In both triangles the turning angle is same Since, the speed is constant the magnitude of velocity is same, length of vector vi and v2 is same. Since d0 is very- very small we can assume that is perpendicular to V
atangential change in speed along circumference time AT ' dt dv Angular acceleration =Ao-Rx at. Tangential acceleration changes Speed and centripetal acceleration changes direction. acP