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,
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=${v_{outer}}/{v_{inner}}=2$
1 comment:
rious more interest in some of them hope you will trigonometric application
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