Relation between Linear and Angular velocity
As we know,
[Tex]|v| = r\frac{\Delta \theta }{\Delta t} [/Tex] . . .(1)
[Tex]\left[\omega =\frac{\Delta \theta }{\Delta t} \right] [/Tex] . . .(2)
Using, (1) and (2) we get,
[Tex]|v| = \frac{\Delta r\theta }{\Delta t} [/Tex]
As r is the radius of the circular path,
[Tex]|v| = r\frac{\Delta \theta }{\Delta t} = r \omega \quad \left[\omega =\frac{\Delta \theta }{\Delta t} \right] [/Tex]
Thus,
|v| = rω
Hence, it is the required relation between Linear and Angular velocity.
Note: Using this relation, we can find the relation between Linear and Angular Acceleration, i.e.,
The following table shows all the relations, between linear and circular motion,
Circular | Linear | Relation |
---|---|---|
θ | S | θ = Sr |
ω | v | ω = v/r |
α | a | α = a/r |
Uniform Circular Motion
Uniform Circular Motion as the name suggests, is the motion of a moving object with constant speed in a circular path. As we know, motion in a plane only has two coordinates, either x, and y, y and z, or z and x. Except for Projectile motion, circular motion is also an example of motion in a 2-D plane.
In a uniform circular motion, the object moves with constant speed but not with constant velocity as the direction of the motion is due to the circular path always changing. From the motion of electrons in Bohr’s Atomic model to the motion of the hands of an analog clock, we can see Uniform Circular Motion around us.
In this article, we will learn about the details of Uniform Circular Motion i.e., formulas related to uniform circular motion, examples, and the equation of motion of the uniform circular motion.