Question

Ans. Circular moul
A uniform circular motion is an accelerated motion.
Explain it. State whether the acceleration is uniform
or variable ? Name the force responsible to cause this
acceleration. What is the direction of force at any
instant ? ​

Answer 1

✪ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ✪

Acceleration of a particle is defined as the rate of change of velocity. As velocity is a vector quantity, it can change both its magnitude and direction and acceleration occurs in both cases.

When a particle is in a uniform circular motion, magnitude of its velocity is constant. However the direction of the velocity is changing continuously for every instant. As such, uniform circular motion is an accelerated motion.

★ᴜɴɪғᴏʀᴍ ᴏʀ ᴠᴀʀɪᴀʙʟᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ★

Magnitude of the acceleration experienced by the particle is given by

$a = \frac{v²}{r}$

where v, r are linear velocity of the particle and radius of the circular path respectively.

As v is constant in a uniform circular motion, magnitude of acceleration of the particle is constant in this case. Acceleration seems to be unchanging? But no, this is not the case.

Direction of this acceleration (Centripetal Acceleration) is always towards the center of the circle. As the particle moves, the direction of the center w.r.t the particle continuously changes and so does the direction of acceleration. Because of this change in direction of acceleration, it is not a uniform but a variable acceleration.

᯽ғᴏʀᴄᴇ ʀᴇsᴘᴏɴsɪʙʟᴇ᯽

The force required to cause this acceleration is known as centripetal force. It is given by the expression

$F = m\frac{v²}{r}$

where m is the mass of the particle.

Centripetal force is a force which is required. This required force is provided by various kind of forces in different scenario. Some examples are

• When a car turns on a curve road, friction provides the necessary centripetal force.
• When a mass is rotated by binding a thread to it, the tension in the thread provides the necessary centripetal force.
• When earth rotates around the sun, the gravitational force between sun amd earth provides the necessary centripetal force.
• When electron moves around nucleus(In classical Model of Atom) electrostatic force between electron and nucleus provides the necessary centripetal force.

These are some of the various forces responsible for causing centripetal acceleration in various scenario.

✫ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ✫

As explained above, direction of acceleration in a uniform circular motion is always towards the center of the circular path.

However, if it was a non uniform circular motion, there will be acceleration in the instantenous direction of motion due to change in magnitude of velocity. This acceleration is known as tangential acceleration. In such cases, resultant of the tangential and centripetal acceleration gives the magnitude and direction of the total acceleration.