Uniform Circular Motion MCQ - Practice Questions & Answers

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Uniform circular motion is considered one of the most asked concept.
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Uniform circular motion

Introduction -

Circular motion is one of the examples of motion in two dimensions. In the case of circular motion, the particle moves in a circular path on the circumference of a circle. The velocity of a particle moving on a circular path is along the tangent at that point.

Terms related to circular motion-
Radius vector
Vector joining the centre of the circular path to the position on the circular path is called radius vector

Angular position

Angle made by the radius vector with reference line (arbitrarily chosen diameter) is called angular position.
The direction of angular position can be clockwise or anticlockwise depending upon the choice of frame of reference.
The angular position of the particle at position "P" is denoted by angle $\theta$ in the diagram above.

Angular displacement

The change in angular position is called angular displacement.
It is the angle through which the radius vector rotates during the given circular motion.
The angular displacement between positions 'P' and 'Q' is denoted by $\Delta \theta$ in the diagram above.
S.I unit of angular position and angular displacement is Radian.

Angular velocity

Denoted by $\omega$ (omega)
$\omega$ -Rate of change of angular displacement.
Average angular velocity-
$\omega _{avg}=\frac{\Delta \theta }{\Delta t}$
Instantaneous angular velocity-
$\omega = \frac{d\theta }{dt}$
S.I. units- Radian per second (rad per sec )
$\omega$ is a vector quantity
The direction of $\omega$ is given by the Right-hand rule.
According to the right-hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then the thumb will point the direction of the angular velocity.
Relation between angular velocity and linear velocity-
$\vec{v} =\vec{\omega} \times \vec{r}$

3. Angular Acceleration

The rate of change of angular velocity with time is said to be Angular Acceleration.
$\alpha =\frac{\Delta \omega }{\Delta t}$
SI units- $rad.(sec)^{-2}$
Angular Acceleration is a vector quantity.
The direction of Angular Acceleration

a) If angular velocity is increasing then the direction of Angular Acceleration

is in the direction of angular velocity.

b) If angular velocity is decreasing then the direction of Angular Acceleration

is in the direction which is opposite to the direction angular velocity.

4. Time period-

Time is taken to complete one rotation
Formula-

$T=\frac{2\pi }{\omega }$

Where $\omega=\text {angular velocity }$

If N= no. of revolutions and t=total time then

$T=\frac{t }{N }$ or $(\omega =\frac{2\pi N}{t})$

S.I unit seconds (s)

5. Frequency-

The total number of rotations in one second.
Formula-

$\nu = \frac{1}{T}$

S.I. unit = Hertz
We can write relation between angular frequency and frequency as

$w= 2\pi \nu$

6. Centripetal acceleration and Tangential acceleration -

a. Centripetal acceleration-

When a body is moving in a uniform circular motion, a force is responsible to change the direction of its velocity.This force acts towards the centre of the circle and is called centripetal force. Acceleration produced by this force is centripetal acceleration.
Formula-

$a_c=\frac{V^2}{r}$