Circular or Rotational MotionCircular motion is a movement of an object

along the circumference of a circle or rotation along a circular path or a circular orbit. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations describing circular motion of an object do not take size or geometry into account, rather, the motion of a point mass in a plane is assumed.

It can be uniform, that is, with constant angular rate of rotation (and thus constant speed), or non-uniform, that is, with a changing rate of rotation.

Example of Circular or Rotational Motion

FORMULAS FOR UNIFORM CIRCULAR

MOTION

Circumference of the circle

C = 2π r.

Angular rate or angular velocity

*Angular velocity is measured in radians / second, although for motors in particular it is commonly expressed in rpm (revolutions per minute).

Speed of the object traveling the circle

Angle θ swept out in a time t

Acceleration due to change in the direction

The axis of rotation is shown as a vector Ω perpendicular to the plane of the orbit and with a magnitude ω = dθ / dt. The direction of Ω is chosen using the  right-hand rule. With this convention for depicting rotation, the velocity is given by a vector  cross product  as

which is a vector perpendicular to both Ω and r ( t ), tangential to the orbit, and of magnitude ω r. Likewise, the acceleration is given by

which is a vector perpendicular to both Ω and v ( t ) of magnitude ω |v| = ω2 r and directed exactly opposite to r ( t ).

WHERE : Ω = represents the rotation to the plane

of the orbit.C = circumferenceΩ = angular rate or angular velocityT = period for one rotationr = radiusv = speedt = time

Circular motion is accelerated even if the angular rate of rotation is constant, because the object's velocity vector is constantly changing direction. Such change in direction of velocity involves  acceleration of the moving object by a  centripetal force, which pulls the moving object toward the center of the circular orbit. Without this acceleration, the object would move in a straight line, according to  Newton's laws of motion.

According to the right hand rule. If the object is in counter-clockwise ("anti-clockwise") horizontal circular motion (as viewed from above), then the angular velocity vector will point vertically upward. In the absence of gravity, the centripetal force will be horizontal, in the plane of motion, pointing towards the center of the circle. If you're taking a downward gravitational force into account, then the centripetal force will be inward but also upward. The object will move upward if the vertical component of the centripetal force is greater than the object's gravitational weight.

Example of Right-Hand Rule

Presented by:

Jessica Elaine M. Palo

Meryll Elijah C. Mendoza

Benyna Ninez L. Bausas

Eloisa A. Caisip

Shaira Marie T. Vasquez

Presented to: Mrs. Gliceria Quizon (Physics Teacher)

THANKS FOR WATCHING!!!