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PHYSICS for NEET and JEE Pradeep Kshetrapal Class XI Portion
Chapter 4- Motion in a Plane Centripetal Acceleration Phy-XI-4-12
CENTRIPETAL ACCEELRATION We know that, a body moving in a straight path will continue to move in straight path unless an external force is applied on it. This is law of inertia. 1 Apply acceleration. -> The direction of acceleration decides either of the three results.
(i) Whether Velocity will increase. (ii) Whether Velocity will decrease. (ii) Direction of velocity will change or not. (i) If the acceleration is in the direction of velocity, then velocity will increase. v-u + at
If the acceleration is in the direction opposite to the direction of initial velocity then the velocity will decrease. Ua If we apply the acceleration in the direction 900 to the direction of velocity then it will change the direction of motion. V-U+ t v-0 + at. at Resultant velocity v
In case of earth a body start moving with a3-* velocity VH in horizontal direction. If the acceleration due to gravity is applied on it then, it will continuously f change the direction of l ion motion. It will form a parabolic path t Gravity-free Path Projectile Motion
A body is moving in a horizontal direction and we apply an acceleration always perpendicular to its direction of velocity, then the resultant we getis the continuous change in the direction of motion. VH gt gt Again we apply acceleration at right angle to the direction of velocity and so on we will get the figure shown below
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.
Centre oVelocity acceleration
This acceleration is acting towards centre thus it is known as centripetal acceleration The acceleration which tends an object to move into a circle is known as centripetal acceleration. Its direction is towards centre of the circle. A straight moving object cannot turn into circle unless centripetal acceleration is applied Similarly an object moving in circle definitely has a centripetal acceleration.
indicates change in velocity 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 Av At
AV Now acceleration a is - Therefore direction of is along av (change in velocity). But AV is normal to V (velocity) Hence acceleration is perpendicular to velocity of particle. Velocity is tangential to circumference, hence acceleration is normal to surface that is towards centre.
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
Net acceleration is resultant of the two linear accelerations l acP