Uniform circular motion

Article about the Uniform circular motion

In everyday life, we often encounter objects that move in a uniform circular motion. One example of an object that undergoes uniform circular motion is the second needle, the minute needle, and the clock needle on the analog clock. The second needle always rotates at an angle of 360^o for 60 seconds (one minute) or rotates at a 6^o angle for one second. The minute needle always rotates at a 360^o angle for 60 minutes (one hour) or rotates at a 6^o angle for one minute. Hour needle also always rotates 360^o for 24 hours (one day). If an object moves in a regular circle such as a second needle, a minute needle, or a clock needle then the objects are said to be doing the circular motion. Can you think of examples of objects that move in a circular motion?

Definition of the uniform circular motion

Uniform circular motion has two meanings. First, an object is said to do nonuniform circular motion if as long as the object moves in a circle, the speed of the object is always constant or the speed of each part of the object is always constant. Second, an object is said to be doing a uniform circular motion if the angular velocity of the object is always constant. Angular velocity is a vector quantity. Therefore, angular velocity consists of the magnitude and direction of the angular velocity. To better understand the meaning of the uniform circular motion, look at the following illustration.

Angular velocity (ω) is constant

Review the second needle on an analog wall clock. When the second needle rotates, all parts of the second needle, both those located at the end, in the middle, and near the axis, rotate together. Because all parts of the second needle rotate together then when the second needle rotates at an angle of 360^o (one revolution), all parts of the second hand also rotate at an angle of 360^o (one revolution). When the second needle takes a 36^o (one revolution) angle for 60 seconds (one minute), all parts of the second needle also rotate the 360^o angle for 60 seconds (one minute).

The angular speed of the second needle is 6 ^o/s.

ω = angular speed, θ = angle, t = time

The angular speed of the second needle is always 6 ^o/s and the direction of the angular velocity (direction of rotation) of the second needle is always constant.

Speed (v) is constant

When the second needle rotates for 60 seconds (one minute), all parts of the second needle, either close to the axis or far from the axis also rotate for 60 seconds (one minute). Although the time interval of all parts of the second needle is the same, ie 60 seconds, the length of the trajectory that passed through each part of the second needle varies. The part of the second needle that is close to the axis has a shorter trajectory, whereas the part of the second needle that is far from the axis has a longer trajectory.

v = speed, d = length, t = time interval, T = period (time needed to rotate one round), r = distance from the axis of rotation.

Based on the formula of the speed, it can be concluded that the speed of each part of the second needle depends on its distance from the axis of rotation (r). The farther from the axis (large r), the greater the speed. Although the speed of each part of the needle is different, the speed of each part of the needle is always constant.

Centripetal acceleration

There are two types of acceleration in a circular motion, namely angular acceleration and linear acceleration. Angular acceleration occurs when the angular velocity (angular velocity) or direction of angular velocity changes. Instead of linear, acceleration occurs when the speed or direction of speed changes. In the uniform circular motion, the angular velocity and direction of angular velocity are always constant. Therefore, there is no angular acceleration in the uniform circular motion. In the uniform circular motion, only speed is always constant. The direction of speed is continually changing or not constant. Because the direction of linear velocity is constantly changing, there must be a linear acceleration in the uniform circular motion.

Acceleration that occurs due to changes in the velocity direction is called the centripetal acceleration. Centripetal acceleration is also called radial acceleration. Centripetal acceleration or radial acceleration is one type of linear acceleration. Centripetal acceleration is a vector quantity. Therefore, centripetal acceleration has a magnitude and direction.

Magnitude of the centripetal acceleration:

a_c = magnitude of the centripetal acceleration

v = speed

r = distance from axis

ω = angular speed

Conceptual questions and answer about Uniform circular motion

1. Question: What is meant by uniform circular motion? Answer: Uniform circular motion refers to the motion of an object moving at a constant speed in a circular path.
2. Question: What kind of acceleration does an object in uniform circular motion experience? Answer: An object in uniform circular motion experiences a centripetal acceleration that is always directed toward the center of the circular path.
3. Question: How does the velocity of an object in uniform circular motion change? Answer: In uniform circular motion, the magnitude of the velocity remains constant, but its direction continuously changes, hence the velocity is not constant.
4. Question: State and explain the formula for the magnitude of the centripetal acceleration. Answer: The formula for the magnitude of the centripetal acceleration is a = v²/r, where v is the speed of the object and r is the radius of the circular path. This formula represents the fact that the acceleration is directly proportional to the square of the speed and inversely proportional to the radius.
5. Question: What provides the centripetal force for a planet orbiting the sun? Answer: The gravitational force between the planet and the sun provides the centripetal force that keeps the planet moving in its orbit.
6. Question: What would happen to a planet’s speed as it moves closer to the sun in its elliptical orbit? Answer: According to Kepler’s second law (the law of areas), a planet moves faster when it is closer to the sun and slower when it is further away.
7. Question: In what scenario does the centripetal force become zero for an object moving in a circular path? Answer: If the object is released from its circular path, the centripetal force becomes zero as there is no longer any force pulling the object towards the center.
8. Question: What role does friction play in the uniform circular motion of a car moving around a curve? Answer: When a car is moving around a curve, friction between the tires and the road provides the necessary centripetal force to keep the car moving in a circular path.
9. Question: Can an object be in equilibrium in uniform circular motion? Answer: No, an object in uniform circular motion is not in equilibrium because there is a net force acting on it (the centripetal force) and a constant change in the direction of its velocity.
10. Question: What is the direction of the velocity vector at any point in the circular path? Answer: At any point in the circular path, the velocity vector is tangent to the circle and in the direction of motion.
11. Question: How can you increase the centripetal acceleration of an object in uniform circular motion? Answer: Centripetal acceleration can be increased by increasing the speed of the object or by decreasing the radius of the circular path.
12. Question: Is it possible for an object to have a constant speed but still be accelerating? Explain with reference to uniform circular motion. Answer: Yes, in uniform circular motion, an object moves with a constant speed but its velocity is not constant because its direction is continuously changing. The change in velocity implies an acceleration (the centripetal acceleration).
13. Question: Is there any work done by the centripetal force on an object in uniform circular motion? Answer: No, the work done by the centripetal force is zero because the force is perpendicular to the direction of motion, and work is defined as the component of force in the direction of motion.
14. Question: What happens to an object in uniform circular motion if the centripetal force suddenly disappears? Answer: If the centripetal force suddenly disappears, the object would move off in a straight line tangent to the circular path, following Newton’s first law of motion.
15. Question: What’s the formula for centripetal force? Answer: The formula for the centripetal force is F = mv²/r, where m is the mass of the object, v is the speed, and r is the radius of the circular path.
16. Question: How does mass of an object affect the centripetal force in uniform circular motion? Answer: The centripetal force is directly proportional to the mass of the object. If the mass increases, the centripetal force will also increase, given the speed and the radius stay constant.
17. Question: Does the period of rotation depend on the mass of the object in uniform circular motion? Answer: No, the period of rotation doesn’t depend on the mass of the object. It only depends on the speed of the object and the radius of the circular path.
18. Question: What is the difference between centrifugal force and centripetal force? Answer: Centripetal force is the real force that acts towards the center of the circle causing circular motion. Centrifugal force, on the other hand, is a fictitious force observed in a rotating frame of reference, that acts outward, away from the center of rotation.
19. Question: Why doesn’t the centripetal force do any work in uniform circular motion? Answer: The centripetal force doesn’t do any work in uniform circular motion because the force is always perpendicular to the displacement of the object. Since work is the dot product of force and displacement, and the cosine of 90 degrees is zero, no work is done.

20. Question: Can the speed of an object in uniform circular motion change? Answer: In uniform circular motion, the speed of the object is constant. However, if the speed were to change, it would no longer be considered uniform circular motion. It would instead be considered non-uniform circular motion, which involves both centripetal and tangential acceleration.