2.5 Motion in Circle(basics)

In this section we study the cicular motion.

We have definitely seen circular motion in our daily lives.



How do we understand/define circular motion?

-"In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation."-wikipedia

Before going into the details of the circular motion lets understand some basic terminologies.

Measure of angle/(Radian): Consider the following circle.


Then the radian measure of an angle($\theta$) is defined to be as follows,
$$\theta=\frac{s}{r}$$ where, $s$=arc length from point A to B 
    and $r$=radius

Therefore, it is clear that a unit radian is the angle subtended by an arc length equal to the radius of the circle. The SI unit is the radian(rad). Click here to learn more.

Angular Velocity: "The angular velocity of the particle is the measure of the rate of change of its angular displacement with respect to time."
$$\omega=\frac{\theta}{t}=\frac{2\pi}{T}$$where, $\theta$=angle measured in radian,
         $t$=time taken to subtend angle $\theta$  (measured in seconds)        
  and $T$=time taken for a complete revolution (measured in seconds) 

Relation between linear velocity and angular velocity: 
$$v=\omega r$$

 Here's an easy to follow video example,

 

Exercise: Given a circle of 3cm, and consider an arc length of 5cm. How much angle does an arc subtend?
Soln: 1.667 rad

Exercise: Consider the given diagram below. Find the ratio of the linear velocity of the outer ball to the inner ball placed at half the radius of the turntable.
Soln: Ratio=${v_{outer}}/{v_{inner}}=2$



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