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Question: Let \({a_r}\,\)and \({a_t}\) represent radial and tangential acceleration . the motion of particle m...

Let ar {a_r}\,and at{a_t} represent radial and tangential acceleration . the motion of particle may be circular if : ( assume that only momentary rest is allowed)
A. ar=at=0{a_r} = {a_t} = 0
B. ar=0 and at≠0{a_r} = 0\,and\,{a_t} \ne 0
C. ar≠0 and at=0{a_r} \ne 0\,and\,{a_t} = 0
D.ar≠0 and at≠0{a_r} \ne 0\,and\,{a_t} \ne 0

Explanation

Solution

In order to answer this question let us first know about circular motion . The movement of an object around the circumference of a circle, or rotation around a circular direction, is known as circular motion. It can be either uniform (with a constant angular rate of rotation and speed) or non-uniform (with a changing rate of rotation). The equations of motion explain how a body's centre of mass moves. The distance between the body and a fixed point on the surface remains constant in circular motion.

Complete step by step answer:
The term "acceleration" refers to the rate at which velocity changes. The net acceleration in a rotational motion has two components: one Normal (along the radius) and one Tangential (along the axis) (along the circumference). The normal acceleration is used to make the motion circular, while the tangential acceleration will speed up or slow down the rotation. The tangential part of acceleration is zero since a uniform motion is defined as a constant velocity motion (i.e. the rotation is moving at a constant speed). If the rotation is non-uniform, the speed of rotation is changing, implying that the tangential portion of the net acceleration is changing as well.
The tangential acceleration is at{a_t}the normal acceleration is ar{a_r}and the pseudo-acceleration due to the body's inertia is ac{a_c}
Now, getting to the question,
The cause of a particle moving faster or slower in a circular motion is tangential acceleration. A uniform motion is defined as a motion with a constant velocity. As a result, the tangential part of acceleration is equal to zero.
The centripetal acceleration of an object travelling in a circular direction at a constant speed is constant. The radial acceleration, however, is not constant due to the constant change of direction.
As a result, ar≠0 and at=0{a_r} \ne 0\,and\,{a_t} = 0
Hence the correct option is: (C) ar≠0 and at=0{a_r} \ne 0\,and\,{a_t} = 0

Note: The fundamental relationship between moment of inertia and angular acceleration is that the greater the moment of inertia, the lower the angular acceleration. The moment of inertia of an object is determined not only by its mass, but also by its mass distribution relative to the axis around which it rotates.