The motion of the body moving along a circular path is an example of ______.
accelerated motion
Understanding Motion Along a Circular Path
The question asks about the type of motion a body exhibits when moving along a circular path. To answer this, we need to understand different types of motion and key physics concepts like velocity and acceleration.
Velocity and Acceleration in Circular Motion
Velocity is a vector quantity. This means it has both magnitude (speed) and direction. Acceleration is defined as the rate of change of velocity. Since velocity has both magnitude and direction, acceleration can occur if either the speed changes, or the direction changes, or both.
When a body moves along a circular path, its direction of motion is continuously changing. At any point on the circle, the velocity vector is tangent to the circle at that point. As the body moves, the direction of this tangent vector changes.
Why Circular Motion is Accelerated
Even if the body moves at a constant speed along the circular path (this is called uniform circular motion), its velocity is still changing because its direction is changing. Since velocity is changing, there must be acceleration. This acceleration is directed towards the center of the circle and is called centripetal acceleration.
So, whether the speed is constant or changing, motion along a circular path always involves a change in direction, which means the velocity is changing, and therefore the motion is accelerated.
Analyzing the Options
- Decelerated motion: This means the speed is decreasing. Circular motion can be decelerated if the speed is reducing while moving in a circle, but not all circular motion is decelerated.
- Accelerated motion: This means the velocity is changing. As explained, the velocity in circular motion always changes direction, leading to acceleration. If the speed also changes, there is additional acceleration. Therefore, circular motion is always accelerated motion.
- Non-uniform motion: This typically refers to motion where the speed is not constant. Circular motion can be non-uniform if the speed is changing. However, even uniform circular motion (constant speed) is a type of accelerated motion. So, non-uniform motion is a possible characteristic, but 'accelerated motion' is a more fundamental description of any circular motion.
- Uniform motion: This typically refers to motion with constant speed in a straight line (constant velocity). In the context of circular motion, 'uniform circular motion' means constant speed. However, even uniform circular motion is accelerated because the direction changes. So, general circular motion is not uniform motion in the sense of constant velocity.
Based on the definition of acceleration (change in velocity) and the nature of motion along a circular path (continuous change in direction), circular motion is always an example of accelerated motion.
| Type of Motion | Velocity (Magnitude & Direction) | Acceleration |
|---|---|---|
| Linear Motion (Constant Velocity) | Constant magnitude, Constant direction | Zero |
| Linear Motion (Changing Velocity) | Changing magnitude OR Constant magnitude & Changing direction (e.g., bouncing) OR Both | Non-zero |
| Circular Motion (Uniform Speed) | Constant magnitude, Changing direction | Non-zero (Centripetal acceleration) |
| Circular Motion (Changing Speed) | Changing magnitude, Changing direction | Non-zero (Tangential and Centripetal acceleration) |
Since the motion along a circular path involves a change in the direction of velocity, it is inherently accelerated motion, even if the speed is constant.
Revision Table: Key Motion Concepts
| Concept | Definition | Involves Change In |
|---|---|---|
| Velocity ($\vec{v}$) | Rate of change of position | Position ($\vec{r}$) |
| Speed ($|\vec{v}|$) | Magnitude of velocity | Distance travelled per unit time |
| Acceleration ($\vec{a}$) | Rate of change of velocity | Velocity ($\vec{v}$) (either magnitude or direction or both) |
Additional Information on Circular Motion Physics
In uniform circular motion, where the speed $v$ is constant and the radius of the path is $r$, the magnitude of the centripetal acceleration $a_c$ is given by the formula:
$$a_c = \frac{v^2}{r}$$
This acceleration is always directed towards the center of the circle. If the speed is changing (non-uniform circular motion), there is also a tangential acceleration $a_t$, which is parallel or anti-parallel to the velocity vector and changes the speed. The total acceleration is the vector sum of the centripetal and tangential accelerations.
The fact that there is always a centripetal acceleration (due to the change in direction) means that any motion along a circular path is accelerated motion.
Important Questions from Motion
The motion of a particle of mass m is described by the relation, y = ut - 1⁄2 gt2, where u is the initial velocity of the particle. The force acting on the particle is
The motion of ______ body is an example of uniformly accelerated motion.
- in a particular direction is velocity.
Motion of an object is if its velocity is constant.
______ time graph shows speed of an object.
