Uniform Circular Motion - Practice Questions & MCQ

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Quick Facts

Uniform circular motion is considered one of the most asked concept.
28 Questions around this concept.

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For a particle in a uniform circular motion, the acceleration $\bar{a}$ at a point $P(R,\Theta )$ on the circle of radius R is

(Here $\Theta$ is measured by x-axis)

$\frac{\upsilon^{2} }{R}\hat{i}+\frac{\upsilon^{2} }{R}\hat{j}$

$-\frac{\upsilon^{2} }{R}\cos \Theta \hat{i}+\frac{\upsilon^{2} }{R}\sin \Theta \hat{j}$

$-\frac{\upsilon^{2} }{R}\sin \Theta \hat{i}+\frac{\upsilon^{2} }{R}\cos \Theta \hat{j}$

$-\frac{\upsilon^{2} }{R}\cos \Theta \hat{i}-\frac{\upsilon^{2} }{R}\sin \Theta \hat{j}$

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Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is:

m₁r₁ : m₂r₂

m₁: m₂

r₁: r₂

1 : 1

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Concepts Covered - 1

Uniform circular motion

Introduction -

Circular motion is one of the examples of motion in two dimensions. To cause a body to have a circular motion, it must be given some initial velocity and there is a force must act on the body which is always directed at right angles to instantaneous velocity. The body moves in circular path have direction of velocity in the tangential direction of the circular motion always.

Terms related to circular motion-

Angular Displacement

For a circular motion angular displacement is defined as the angle in radians (degrees, revolutions) through which a point has been rotated about a point or specified axis.
Denoted by (theta)
S.I unit is Radian

Angular velocity

Denoted by $\omega$ (omega)
$\omega$ -Rate of change of angular displacement.
$\omega = \frac{\Theta }{t}$ or $\omega = \frac{d\Theta }{dt}$
S.I. units- Radian per second (rad per sec )
$\omega$ is a vector quantity
Direction of $\omega$ is given by 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 thumb will point the direction of the angular velocity.

Fig. Shows angular velocity

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.
Direction of Angular Acceleration

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

is in the direction of angular velocity.

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

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

4. Time period-

Time taken to complete one rotation
Formula-

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

Where

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-

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-

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