Question

How does uniform circular motion differ from a uniform linear motion?

Answer 1

Hint: Uniform motions are those which have a constant speed. In circular motion, though the magnitude of velocity is a constant, the direction of velocity is changing. Also, a straight line motion is one dimensional

Complete step-by-step answer:
Uniform motion is one in which a particle is moving at a constant speed. In linear motion, the particle moves along a straight line.
So $\vec v = {\text{constant}}$
We know the momentum of a particle of mass $m$ moving with velocity $\vec v$ js
$\vec p = m\vec v$.
So we can see the following differences between a uniform-linear motion and a uniform circular motion.

Uniform linear motion
i. In the case of uniform linear motion, the speed of the particle is not changing and also, its direction of motion is fixed.
ii. For an object with constant mass, the direction and magnitude of momentum always remain constant.
iii. Since the magnitude and direction of momentum are not changing, Newton's first law suggests that no force is required to keep the particle moving. So the net force on the particle is zero.
iv. A uniform linear motion happens along a straight line and hence, it is a one-dimensional motion.

Uniform circular motion
i. In a circular motion, the direction of the motion of the particle is continuously changing. The particle always moves along the tangent of the circle at a constant speed. So even though the speed of the particle does not change, we are constantly changing its direction of motion.
ii. Since the velocity vector changes its direction continuously, we see that the momentum is also changing its direction continuously.
iii. To constantly change the direction of momentum, a force is necessary. This force is called the centripetal force and it is a necessity for circular motion. In the absence of this force, the particle would simply move tangentially in a uniform linear motion.
iv. A circle is a two-dimensional figure and hence circular motion happens in 2 dimensions.

Additional information
The magnitude of the centripetal force is given as ${F_c} = m\dfrac{{{v^2}}}{r}$ and for a circular motion, it always acts towards the centre of the circle. For curves other than a circle, it acts towards the centre of curvature of that point. The Centre of curvature is the centre of a circle that is just tangential to the curve at that point.

Note: For a particle moving uniformly to experience no force, It is necessary that the mass of the body is not changing. But it is always true that the acceleration of a body under uniform linear motion is zero.