Uniform Circular Motion

Aliens have kidnapped your friend and they have kept her in a circular moving object. You need to save her but you don’t know how the thing works. In order to save her, you must understand the mechanics of this weird circular moving object so that you can defeat it. Let us help you with the basics of circular motion.

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Uniform Circular Motion

Circular motion is the motion of a body following a circular path. Uniform circular motion is a specific type of circular motion in which the motion of a body following a circular path is at a constant speed. The body has a fixed central point and remains equidistant from it at any given position.

When an object goes around in a circle, the description of its motion becomes interesting in many ways. To better understand the circular motion let us look at an example.

Suppose you have a ball attached to a string and you move it constantly in a circular motion. Then we observe two things:

1. The speed of the ball is constant. It traces a circle with a fixed center.
2. At every point of its motion, the ball changes its direction. Therefore, we can say that in order to stay on a circular path, the ball has to change its direction continuously.

From the second point, an important result follows. Newton’s first law of motion tells us that there can be no acceleration without a net force. So there must be a force associated with the circular motion. In other words, for the circular motion to take place a net force has to act on the object. Thus, the change in direction is a result of a centripetal force.

Centripetal force is the force acting on a body in a circular path. It points towards the center around which the body is moving.  

As long as the ball is attached to the string, it will continue to follow the circular path. The moment the string breaks or you let go of the string, the centripetal force stops acting and the ball flies away.

Browse more Topics under Motion

• Introduction to Motion and its Parameters
• Graphical Representation of Motion
• Equations of Motion

Learn more about Motion in Different Acceleration for Different Time Intervals.

Terminologies of Uniform Circular Motion

To study uniform circular motion, we define the following terms.

Time Period (T)

Time period (T) is the time taken by the ball to complete one revolution. It is denoted by ‘T’. If ‘r’ is the radius of the circle of motion, then in time ‘T’ our ball covers a distance = 2πr. Let us assume the ball takes 3 seconds to complete one revolution. So T= 3 secs.

Frequency (f)

The number of revolutions our ball completes in one second is the frequency of revolution. We denote frequency by f and f = 1/T. The unit of frequency is Hertz (Hz). One Hz means one revolution per second. Here the frequency will be 1/3 Hz.

Centripetal Force

We saw earlier that a body moving in a circle changes its direction continuously. Therefore, we said that circular motion is an accelerated motion. From Newton’s laws, we know that a body can accelerate only when acted upon by some force.

In the case of circular motion, this force is the centripetal force. If ‘m’ is the mass of the body, then the centripetal force on it is given by F = mv²/r; where ‘r’ is the radius of the circular orbit.

Angular Speed

We can also get an idea of how fast an object is moving in a circle if we know how fast the line joining the object to the center of the circle is rotating. We measure this by measuring the rate at which the angle subtended at the center changes. This quantity is ω and ω = Change in angle per unit time. Hence, ω is the Angular Speed.

The SI unit is radian / s or rad/s. For a single rotation, the change in angle is 2π and the time taken is ‘T’, therefore we can write:

ω = 2π/T = 2πν …(4)

It is usually measured in r.p.m or rotations per minute. ω = 1 r.p.m, if a body completes one rotation per minute. Also we can convert r.p.m to radians per second as i r.p.m.  = 2π/60s = π/30 rad/s

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Solved Examples For You

Q: A car runs at a constant speed on a circular track of radius 100 m taking 62.8 s on each lap. What are the average speed and average velocity on each complete lap? (π=3.14)

1. velocity = 10 m/s and speed = 10 m/s
2. speed = 10 m/s and velocity = 0 m/s
3. velocity = 0 m/s and speed = 0 m/s
4. velocity = 10 m/s and speed = 0 m/s

Solution: B). Even without solving the problem, a closer look will tell you that all other options may be wrong. As in a circular motion, if the particle returns to the starting position, then the displacement is 0. Thus, for such motion, the velocity is 0 and the speed is non-zero. Furthermore, the circumference of each lap is  2(3.14)(100) which is equal to 628 m. Therefore, speed after each lap is 628/62.8 which is equal to 10 m/s