Question

Let \[{a_r}{\text{ }}{a_t}\] ​ represent radial and tangential accelerations. The motion of a particle may be circular if
A)\[{a_r} = {a_t} = 0\]
B)\[{a_r} = 0\,and\,{a_t} \ne 0\]
C) \[{a_{r}} \ne 0\,and\,{a_t} = 0\]
D) None of these

Answer 1

Hint: The object’s movement about the circumference of a circle, or rotation around a circular direction, is known as circular motion. It can be uniform along with a continuous angular rate of rotation and speed or non-uniform with a varying rate of rotation. The equations of motion describe how the center of mass of a body moves. In a circular motion, the distance from the body and a fixed point on the surface will remain constant.

Complete step by step solution:
The term acceleration states the rate at which velocity fluctuates. The total acceleration in a rotational motion has two components, one is normal along the radius and the other one is tangential along the axis and the circumference. The normal acceleration is applicable to create the motion circular, whereas the tangential acceleration increases or decreases the speed of the rotation. The tangential part of acceleration is zero because a uniform motion is described as a constant velocity motion where the rotation is moving at a constant speed. Tangential acceleration $ = {a_t}$ , Normal acceleration is $ = v$and the false acceleration due to the body's inertia $ = {a_c}$, now from the question we get, the reason for a particle to move faster or slower in a circular motion is because of tangential acceleration. A uniform motion can be described as a motion that has a constant velocity. This results in the tangential part of acceleration becoming equal to zero.
The centripetal acceleration of an object moving in a circular path at a constant speed is constant. But the radial acceleration is not constant because of the constant change of direction.
Hence, ${a_r} \ne 0\,{\mkern 1mu} and{\mkern 1mu} {a_t} = 0$.
The answer is Option C .

Note:
The basic relationship between the moment of inertia and angular acceleration is that as the moment of inertia increases, its angular acceleration decreases. The moment of inertia of an object is found by its mass, and also its mass distribution relative to the axis about which it rotates. If the rotation is non-uniform, the speed of rotation differs, indicating that the tangential portion of the net acceleration is varying too.