Examples of circular motion in the following topics:

 Nonuniform circular motion denotes a change in the speed of a particle moving along a circular path.
 What do we mean by nonuniform circular motion?
 The answer lies in the definition of uniform circular motion, which is a circular motion with constant speed.
 The circular motion adjusts its radius in response to changes in speed.
 This means that the radius of the circular path is variable, unlike the case of uniform circular motion.

 Uniform circular motion describes the motion of an object along a circle or a circular arc at constant speed.
 Therefore, uniform circular motion indicates the presence of a net external force.
 The equation for the acceleration $a$ required to sustain uniform circular motion is:
 In uniform circular motion, the centripetal force is perpendicular to the velocity.
 Develop an understanding of uniform circular motion as an indicator for net external force

 Uniform circular motion is a motion in a circular path at constant speed.
 Under uniform circular motion, angular and linear quantities have simple relations.
 Under uniform circular motion, the angular velocity is constant.
 Any net force causing uniform circular motion is called a centripetal force.
 For uniform circular motion, the acceleration is the centripetal acceleration: $a = a_c$.

 Simple harmonic motion is produced by the projection of uniform circular motion onto one of the axes in the xy plane.
 Uniform circular motion describes the motion of a body traversing a circular path at constant speed.
 There is an easy way to produce simple harmonic motion by using uniform circular motion.
 A point P moving on a circular path with a constant angular velocity ω is undergoing uniform circular motion.
 Describe relationship between the simple harmonic motion and uniform circular motion

 For example, consider the case of uniform circular motion.
 This is the first advantage of describing uniform circular motion in terms of angular velocity.
 For simplicity, let's consider a uniform circular motion.
 Because $\frac{dr}{dt} = 0$ for a uniform circular motion, we get $v = \omega r$.
 Each particle constituting the body executes a uniform circular motion about the fixed axis.

 Since the magnetic force is always perpendicular to the velocity of a charged particle, the particle will undergo circular motion.
 So, does the magnetic force cause circular motion?
 This is typical of uniform circular motion.
 Uniform circular motion results.
 Describe conditions that lead to the circular motion of a charged particle in the magnetic field

 In circular motion, there is acceleration that is tangent to the circle at the point of interest (as seen in the diagram below).
 In circular motion, centripetal acceleration, ac, refers to changes in the direction of the velocity but not its magnitude.
 An object undergoing circular motion experiences centripetal acceleration (as seen in the diagram below.)
 Centripetal acceleration occurs as the direction of velocity changes; it is perpendicular to the circular motion.
 In circular motion, acceleration can occur as the magnitude of the velocity changes: a is tangent to the motion.

 Helical motion results when the velocity vector is not perpendicular to the magnetic field vector.
 In the section on circular motion we described the motion of a charged particle with the magnetic field vector aligned perpendicular to the velocity of the particle.
 In this case, the magnetic force is also perpendicular to the velocity (and the magnetic field vector, of course) at any given moment resulting in circular motion.
 This produces helical motion (i.e., spiral motion) rather than a circular motion.
 Uniform circular motion results.

 The familiar linear vector quantities such as velocity and momentum have analogous angular quantities used to describe circular motion.
 Similarly, circular motion is motion in a circle.
 The angular velocity has a direction perpendicular to the plane of circular motion, just like a bike axle points perpendicularly to the rotating wheel.
 Constant angular velocity in a circle is known as uniform circular motion.
 A vector diagram illustrating circular motion.

 A force which causes motion in a curved path is called a centripetal force (uniform circular motion is an example of centripetal force).
 A force that causes motion in a curved path is called a centripetal force.
 Uniform circular motion is an example of centripetal force in action.
 where: $F_c$ is centripetal force, $m$ is mass, $v$ is velocity, and $r$ is the radius of the path of motion.
 Angular velocity is the measure of how fast an object is traversing the circular path.