Question

What is uniform circular motion?

Answer 1

Uniform Circular Motion (UCM)

Uniform Circular Motion (UCM) is the motion of a molecule around a circular path.

Consider the above figure:

1. The isosceles triangles OBC and DEF are identical since OB and OC are perpendicular velocity vector sectors, hence the ratio of the length BC to the radial distance is equal to the ratio of the magnitudes of v to $∆t$.
2. The chord BC and the arc BC approach each other as $∆\theta$approach zero, and the chord could be replaced by the arc in the proportion.
3. The molecule's velocity-vector v is constant in magnitude in the figure, but it changes direction through an amount v as the molecule moves from location B to position C, and the circle's radius R sweeps out the angle.
4. Because the particle's speed is constant, the length of the arc BC equal to $v∆t$ if $∆t$ is the time corresponding to $∆\theta$ ; therefore, using the ratio relationship$\frac{v^2}{R}=\frac{∆v}{v}$, from which, approximately$\frac{∆v}{∆t}=\frac{v^2}{R}$.
5. As $∆t$approaches zero, $\frac{v^2}{R}$is the magnitude of the particle's instantaneous acceleration a, which is directed inward toward the circle's center, as seen at the G In the Figure; the above acceleration is recognized as the centripetal acceleration, or the regular (at a perfect angle to the route) component of the acceleration, while the other component, which appears when the particle's speed changes, is tangent to the path.