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Uniform Circular Motion - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

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

  • 27 Questions around this concept.

Solve by difficulty

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)

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:

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- 

  1. 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

                                                                     

  1. 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}

                      Where =Centripetal acceleration,

                      V= linear velocity

                      r = radius

                                                    

                                                                      Figure Shows Centripetal acceleration 

      b. Tangential acceleration -

         During circular motion if the speed is not constant, then along with centripetal acceleration there is also a tangential         

         acceleration,Which is equal to the rate of change of magnitude of linear velocity .

  • Formula-

                         \overrightarrow{a_{t}}= \overrightarrow{r}\times \overrightarrow{\alpha }

                               Where \overrightarrow{a_{t}}= tangential acceleration

                                             r= radius

                                             \alpha = angular \: acceleration

       c. Total acceleration- 

  • Vector sum of Centripetal acceleration and  tangential acceleration is called Total acceleration.

  • Formula- 

                             a=\sqrt{{a_{t}}^{2}+\left (\frac{v^{2}}{r} \right )^{2}}

                                       Where a_{t}= tangential acceleration

                                                   \frac{v^{2}}{r}= centripetal acceleration

       d. Angle between Total acceleration and centripetal acceleration ()

  •   Formula-

                              tan \phi =\frac{a_{t}}{a_{c}}= \frac{r^{2}\alpha }{V^{2}}

                                              Where \alpha= angular acceleration

                                                       V= velocity

                                                         r= radius of circle

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Uniform circular motion

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