Uniform Circular Motion

Explore how objects can accelerate even when moving at constant speed! Discover the fascinating world of circular motion and understand why direction matters as much as speed.

What is Uniform Circular Motion?
When the velocity of an object changes, we say that the object is accelerating. The change in velocity could be due to change in its magnitude or the direction of motion or both.
Can you think of an example when an object does not change its magnitude of velocity but only its direction of motion?
When an object moves in a circular path with uniform speed, its motion is called uniform circular motion. Even though the speed remains constant, the object is still accelerating because its direction is continuously changing!
Rectangular Track
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Direction changes: 4 times
The athlete changes direction at each corner (Aโ†’Bโ†’Cโ†’Dโ†’A)
Hexagonal Track
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Direction changes: 6 times
More sides mean more frequent direction changes
Octagonal Track
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Direction changes: 8 times
Even more sides, even more direction changes
Circular Track
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Direction changes: Continuously!
Infinite sides โ†’ continuous direction change โ†’ uniform circular motion
Activity 7.11
Stone tied to thread moving in circular path. Watch what happens when released!
Speed in Circular Motion
We know that the circumference of a circle of radius r is given by 2ฯ€r. If an object takes t seconds to complete one circular path, the speed v is:
v = 2ฯ€r/t
Where:
v = speed of the object (m/s)
r = radius of the circular path (m)
t = time period for one complete revolution (s)
2ฯ€r = circumference of the circle (m)
This formula shows that even though the object moves at constant speed, it's continuously changing direction, making it an accelerated motion!
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Earth and Moon
The Moon orbits Earth in a nearly circular path. Despite moving at constant speed, it's continuously accelerating toward Earth due to gravitational force.
Natural Circular Motion
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Satellites
Artificial satellites in circular orbits around Earth maintain constant speed but continuously change direction, demonstrating uniform circular motion.
Technological Application
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Cyclist on Circular Track
A cyclist moving at constant speed on a circular track experiences uniform circular motion. The track provides the centripetal force needed to change direction.
Sports Example
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Hammer/Discus Throw
Athletes rotate their body to give circular motion to hammer or discus. When released, the object moves tangentially in the direction it was moving at that instant.
Athletic Application
Motion Controls
100
5
Circumference: 628 m
Time Period: 125.6 s
Angular Velocity: 0.05 rad/s
Explore Uniform Circular Motion
Key Concept: Uniform Circular Motion
When an object moves in a circular path with uniform speed, its motion is called uniform circular motion. Even though the speed (magnitude of velocity) remains constant, the velocity is continuously changing because the direction of motion is continuously changing. This makes uniform circular motion an example of accelerated motion.
From Polygons to Circles
Consider an athlete running on tracks of different shapes:

โ€ข Rectangular track: 4 direction changes per lap
โ€ข Hexagonal track: 6 direction changes per lap
โ€ข Octagonal track: 8 direction changes per lap

As the number of sides increases, the athlete has to change direction more frequently. When the number of sides approaches infinity, the track becomes circular, and the direction changes continuously at every point.
Activity 7.11: Stone and Thread Experiment
  • Take a piece of thread and tie a small stone at one end
  • Hold the other end and move the stone in a circular path with constant speed
  • Observe the motion of the stone - it follows a circular path
  • Release the thread and observe what happens
  • The stone moves along a straight line tangential to the circular path
  • This shows that the direction of motion was changing at every point during circular motion
Speed in Circular Motion
For an object moving in a circular path of radius r, if it takes time t to complete one full revolution:

Distance covered = Circumference = 2ฯ€r
Speed = Distance รท Time = 2ฯ€r รท t

Therefore: v = 2ฯ€r/t

This formula gives us the constant speed of the object, but remember that the velocity (which includes direction) is continuously changing.
Real World Applications
Uniform circular motion is observed in many natural and artificial systems:

โ€ข Celestial Motion: Moon orbiting Earth, planets orbiting the Sun
โ€ข Technology: Satellites in circular orbits, wheels of vehicles
โ€ข Sports: Hammer throw, discus throw, cycling on circular tracks
โ€ข Everyday Life: Hands of a clock, washing machine drum, ceiling fans

In all these cases, the objects maintain constant speed but continuously change direction, making them examples of accelerated motion despite constant speed.
Important Points to Remember
โ€ข Uniform circular motion is accelerated motion even though speed is constant
โ€ข The acceleration is due to continuous change in direction, not speed
โ€ข When released, objects in circular motion move tangentially
โ€ข The centripetal force is required to maintain circular motion
โ€ข Speed = 2ฯ€r/t, where r is radius and t is time period
โ€ข Velocity and speed are different - velocity includes direction