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Uniform circular motion is considered one of the most asked concept.
43 Questions around this concept.
The angular velocity (in radian/sec) of a particle rotating in a circular orbit 100 times per minute is:
A particle is moving in a uniform circular motion, the acceleration at a point P(R,$\theta$) on the circle of radius R is (Here $\theta$ is measured from the X-axis):
If a body moving in a circular path maintains a constant speed of 10 ms-1, then which of the following correctly describes the relation between acceleration and radius?
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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)
Circular motion is an example of
Tangent to the circular path of the body gives -
Which of the following statements is false for a particle moving in a circle with a constant angular speed?
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For a particle moving in a circle with constant angular velocity, which of the following statements is false?
A body of mass 1kg is revo,ved in a horizontal circle of radius 1m with constant speed 3m/s. The angular acceleration of a body is
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
Angular position
Angular displacement
Angular velocity
-Denoted by $\omega$ (omega)
- $\omega$-Rate of change of angular displacement.
- Average angular velocity-
$
\omega_{a v g}=\frac{\Delta \theta}{\Delta t}
$
- Instantaneous angular velocity-
$
\omega=\frac{d \theta}{d t}
$
- 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- $\operatorname{rad.}(\mathrm{sec})^{-2}$
Angular Acceleration is a vector quantity.
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 $\omega=$ angular velocity
If $\mathrm{N}=$ no. of revolutions and $\mathrm{t}=$ total time then
$
T=\frac{t}{N}_{\text {or }} \quad\left(\omega=\frac{2 \pi N}{t}\right)
$
- 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}
$
Where =Centripetal acceleration,
V= linear velocity
r = radius
Figure Shows Centripetal acceleration
b. Tangential acceleration -
acceleration, Which is equal to the rate of change of magnitude of linear velocity.
$
a_t=\frac{\mathrm{d} v}{\mathrm{~d} t}
$
- Relation between angular acceleration and tangential acceleration-
$
\overrightarrow{a_t}=\vec{\alpha} \times \vec{r}
$
Where $\overrightarrow{a_t}=$ tangential acceleration
$\vec{r}=$ radius vector
$\alpha=$ angular acceleration
c. Total acceleration-
The vector sum of Centripetal acceleration and tangential acceleration is called Total acceleration.
Formula-
$
a_n=\sqrt{a_c^2+a_t^2}
$
d. Angle between Net acceleration and tangential acceleration ( $\theta$ )
- From the above diagram-
$
\tan \theta=\frac{a_c}{a_t}
$
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