CIRCULAR MOTION o Clyde Ruemm Joshua Aguillon o Kyna Desiree Bucio o Niczie Flor Laid o Danniela Marie Mozo o Jaynne Lorraine Love Paular

CIRCULAR MOTION In physics, circular motion is rotation along a circle: a circular path or a circular orbit. It can be uniform, that is, with constant angular rate of rotation, or non-uniform, that is, with a changing rate of rotation.

uniform circular motion — circular motion in which the magnitude of the velocity vector remains constant has an inward acceleration vector of magnitude |a| = v 2 /r, where v=|v|. nonuniform circular motion — circular motion in which the magnitude of the velocity vector changes, the radial and tangential components of the acceleration vector are a r = v 2 /r a t = slope of the graph of v versus t

Mathematics of Circular Motion There are three mathematical quantities that will be of primary interest to us as we analyze the motion of objects in circles. These three quantities are speed, acceleration and force. The speed of an object moving in a circle is given by the following equation.

The acceleration of an object moving in a circle can be determined by either two of the following equations. The equation on the right (above) is derived from the equation on the left by the substitution of the expression for speed.

CENTRIPETAL FORCE A force that makes a body follow a curved path. Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force which means "center seeking" force. The force has the magnitude

As a car makes a turn, the force of friction acting upon the turned wheels of the car provides centripetal force required for circular motion. As a bucket of water is tied to a string and spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion. As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.

Calculating Centripetal Force Basic Formula Original Formula: New Formula:

The net force (Fnet) is acting upon an object moving in circular motion is directed inwards. The net force is related to the acceleration of the object (as is always the case) and is thus given by the following three equations:

Example: A cyclist rides around a circular track of radius 159.3m at a speed of 21 m/s. Calculate his centripetal force, assuming his mass is 55kg. where a(centripetal)= v 2 /r F(centripetal)=55 kg x (21 m/s) 2 /159.3 m) F(centripetal)= N

MOTION IN A VERTICAL CIRCLE Motion in a vertical circle is no different in principle of horizontal circle, but the weight of the body has to be treated carefully.