When the motion of a body follows a circular path around a fixed point, it is known as circular motion. Here, uniform circular motion is a particular kind of circular motion where the motion of the body follows a circular path at a constant/uniform speed. The body has a fixed central position and so remains at an equal distance from it at any known point.
When an object moves around in circular motion, there are many distinguishing factors to consider.
Explanation through an Example
You have a ball attached to a string, and you move it uniformly over a circular motion; then, two interesting observations can be made.
The speed of the ball remains constant, tracing the circle over a fixed center point.
The ball remains in motion changing its direction constantly. As such, one can opt to stay on a circular path; the ball must change its direction in a constant manner.
We can gain an important observation from the 2nd point. According to Newton’s first law, there will be no acceleration without a net force. As such, there must be a force entangled with the circular motion. Nevertheless, for a circular motion to happen, the object must be acted by a net force, thereby resulting in the change of direction otherwise known as centripetal force.
Imagine that your friend has been kidnapped by aliens, and they have kept him in an object moving in a circular motion. You will be able to save him, only after understanding the mechanism. This page will help you with the basics of circular motion.
From the above-mentioned theory, as long as your friend is in the field of circular motion, it will continue to follow the circular path. The moment the attachment breaks or you let go, the centripetal force stops acting, and your friend will be detached from the object. Then it will be easier for you to rescue your friend.
Types of Circular Motion
There are two kinds of circular motion that can act upon a body in motion:
Uniform circular motion or UCM,
Non-uniform circular motion
In the case of uniform circular motion, the angular speed & acceleration remains constant, whereas the velocity differs. However, in a non-uniform circular motion, both the angular speed and velocity change.
Uniform Circular Motion Formula
Consider a particle moving in a circle. It will have some acceleration acting at the center. This makes it move around the center position. As acceleration is perpendicular to the velocity, it only changes the direction of velocity, and the magnitude remains unchanged. This is the reason the motion is called uniform circular motion. This is otherwise called centripetal acceleration, and the force that acts towards the center is known as centripetal force.
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So, the centripetal force is the force acting on a body over a circular path. This points toward the center of the body in motion.
Considering the uniform circular motion, the acceleration is:
\[ ar = v^{2}r = \omega ^{2} r\]
where,
a=acceleration, r=radius, v=velocity of the object, ω=angular speed
If the mass of the particle is m, from the 2nd law of motion, you can find that:
\[ F = ma \]
\[Mv^{2}r = m\omega ^{2}r\]
So, if a particle moves in a uniform circular motion:
Its speed is constant
Velocity changes at every instant
No tangential acceleration acts on the body
Radial (centripetal) acceleration = \[ \omega ^{2}r \]
v=ωr
In the case of non-uniform circular motion, the tangential acceleration increases/decreases resulting in the acceleration to be the sum of tangential and radial acceleration.
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Uniform Circular Motion Examples
Below is the following example of uniform circular motion:
An example of uniform circular motion is the motion of artificial satellites around the earth. The satellites stay in the circular orbit around the earth due to gravitational force from the earth.
around the nucleus the motion of electrons. The perpendicular movement to the uniform magnetic field of electrons.
The blade of windmills motion.
With a circular dial, the tip of the second hand of a watch shows uniform circular motion.
A rope tied to the stone and being swung in a circular motion.
A curve in a road, a car turning through.
A gear-train inside turning a gear.
Clock hand motion.
Bicycle wheels of motion.
What is the concept of Uniform Circular Motion?
Uniform circular motion will always be used to describe the magnitude of the velocity. The direction of velocity will change at a constant rate from every place. The object's route will be in the shape of a circle, which represents it. The object will be completed after making multiple journeys around the path in the same length of time at the same spot.
The word circular refers to mobility along a curved path. Circular uniform motion is defined as an item moving along a circular path while covering the same distance along the circumference in the same time interval. The speed remains constant in such continually shifting motions.
The tangential speed will be constant at all points along the circumference in a uniform circular motion. The tangential velocity vector is tangent at all points around the circumference. As a result, the acceleration vector always points towards the center of the circle produced by the object's motion. Because it is at a given radius from a central point, or as a centripetal acceleration, or as a radical acceleration, which indicates that it is central seeking.
What are the learning objectives for Uniform Circular Motion?
You will be able to understand the following by the end of this section:
Of an object moving on a circular path solution for the centripetal acceleration.
Of a particle executing circular motion using the equations of circular motion to find the velocity, speed, and acceleration positioning.
Resulting from non-uniform circular motion explaining the differences between tangential acceleration and centripetal acceleration.
Find the total acceleration vector and evaluate tangential and centripetal equations in a non-uniform circular motion.
A specific type of motion in which an object travels in a circle with a constant speed at a particular time given is known as uniform circular motion. Some examples are a propeller spinning at a constant rate at any point is executing the circular uniform motion, the hour's hand, and the second minute of a watch. To watch all this we must know how to analyze the motion in terms of vectors at a particular period. Although the rotation rate is constant, remarkably, points on these rotating objects are accelerating.
FAQs on Uniform Circular Motion
1. What is uniform circular motion?
Uniform circular motion describes the movement of an object travelling in a circular path at a constant speed. While the speed remains the same, the direction of motion is continuously changing. Because the velocity (which includes both speed and direction) is changing, the object is always accelerating.
2. What are some common examples of uniform circular motion in real life?
Uniform circular motion can be observed in many everyday situations. Some common examples include:
- The motion of the tip of a clock's second hand.
- An artificial satellite orbiting the Earth at a constant height.
- The blades of a fan rotating at a steady speed.
- A car moving at a constant speed around a perfectly circular racetrack.
- An athlete running at a consistent pace on a circular track.
3. Why is uniform circular motion considered an accelerated motion even if the speed is constant?
This is a key concept. Acceleration is the rate of change of velocity, not just speed. In uniform circular motion, the object's direction is constantly changing as it moves along the curve. Since velocity is a vector quantity (having both magnitude and direction), a change in direction means the velocity is changing. This change in velocity results in an acceleration, known as centripetal acceleration, which is always directed towards the centre of the circle.
4. What are the key characteristics of an object in uniform circular motion?
An object in uniform circular motion has several distinct properties:
- The speed of the object remains constant.
- The velocity of the object continuously changes because its direction changes.
- It experiences a constant centripetal acceleration directed towards the centre of the circle.
- A centripetal force must always act on the object to keep it in its circular path.
- The motion is periodic, meaning it repeats over a fixed time interval.
5. How does uniform circular motion differ from non-uniform circular motion?
The main difference lies in the speed. In uniform circular motion, the object moves at a constant speed. In non-uniform circular motion, the speed of the object changes. This means that in non-uniform circular motion, there is not only a centripetal acceleration (changing direction) but also a tangential acceleration (changing speed).
6. What force is necessary to maintain uniform circular motion, and what happens if it disappears?
A force called centripetal force is required to maintain uniform circular motion. This force always acts towards the centre of the circular path. If this force suddenly disappears, the object will no longer travel in a circle. Instead, it will move off in a straight line, tangent to the point on the circle where the force vanished, according to Newton's first law of motion.
7. Why is the work done by the centripetal force in uniform circular motion always zero?
Work is done when a force causes displacement in its own direction. In uniform circular motion, the centripetal force is always directed towards the centre of the circle, while the object's displacement at any instant is along the tangent. This means the force and the displacement are always perpendicular (at a 90° angle) to each other. Because of this, the work done by the centripetal force is always zero.
8. What are the essential formulas used to describe uniform circular motion?
To understand and calculate aspects of uniform circular motion, we use a few key formulas:
- Speed (v): v = 2πr / T, where 'r' is the radius and 'T' is the time period.
- Angular Velocity (ω): ω = 2π / T, which measures the rate of rotation.
- Centripetal Acceleration (a_c): a_c = v² / r = ω²r.
- Centripetal Force (F_c): F_c = mv² / r = mω²r, where 'm' is the mass of the object.
