A particle of mass m is revolving in a horizontal circle of...

A particle of mass $m$ is revolving in a horizontal circle of radius $r$ with constant angular speed $\omega .$ The areal velocity of the particle is
(a) $r^{2} \omega$
(b) $r^{2} \theta$
(c) $\frac{r^{2} \omega}{2}$
(d) $\frac{r \omega^{2}}{2}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Areal Velocity

Areal velocity is the rate at which area is swept out by a line connecting a fixed point (often the center of the circle) to the moving particle. In uniform circular motion, it is calculated as half of the product of the square of the radius and the angular speed. This concept is important in various areas of physics, particularly in orbital mechanics, as it relates to the conservation of angular momentum.

Uniform Circular Motion

Uniform circular motion refers to the motion of a particle along a circular path with constant speed. Even though the speed remains constant, the velocity continuously changes direction, resulting in an acceleration directed towards the center of the circle. This concept is fundamental in understanding motions that involve constant angular displacement over time.

Angular Speed

Angular speed, denoted by ?, is the rate at which an object rotates around a fixed point or axis, typically measured in radians per unit time. In uniform circular motion, it represents the constant rate at which the particle covers the circular path, and it is directly related to the linear speed through the radius of the circle.

Transcript

Please give Ace some feedback