Circular Motion Applied physics full guide
Angular Motion
Important concepts, formulas, units, dimensions and exam-focused key points.
📚 Table of Contents
Circular motion
Definition:If a particle moves in a plane such that the distance from the fixed point (radius vector) remains constant about a fixed point then its motion is called circular motion.
Key Note:Angular displacement is measured in radians in the SI system.
2. Angular Velocity
Definition:Angular velocity is the rate of change of angular displacement with respect to time.
Formula:ω = θ/t
SI Unit:rad/s
Dimension:[M0L0T-1]
Nature:Vector quantity
Key Note:Angular velocity represents how fast an object rotates.
3. Angular Acceleration
Definition:Angular acceleration is the rate of change of angular velocity with respect to time.
Formula:α = Δω/Δt
SI Unit:rad/s2
Dimension:[M0L0T-2]
Nature:Vector quantity
Key Note:Angular acceleration indicates how rapidly angular velocity
changes with time.
4. Centripetal Acceleration
Definition:Centripetal acceleration is the acceleration directed towards the centre of a circular path.
Formula:ac = v2/r
SI Unit:m/s2
Dimension:[M0L1T-2]
Key Note:Centripetal acceleration always acts towards the centre
of the circular path.
Important Formulas
θ = s/r
ω = θ/t
α = Δω/Δt
ac = v2/r
🧠 Remember
- Angular displacement is measured in radian.
- Angular velocity is the rate of change of angular displacement.
- Angular acceleration is the rate of change of angular velocity.
- Centripetal acceleration acts towards the centre.
- Always check the correct SI unit and dimension in numerical problems.
📝 Practice MCQ
1. What is the SI unit of angular displacement?
A. metre
B. radian
C. radian/second
D. degree/second
✓ Correct Answer: B. radian
Explanation:The SI unit of angular displacement is radian (rad).
Explanation:The SI unit of angular displacement is radian (rad).
2. What is the dimension of angular velocity?
A. [M0L0T-1]
B. [M0L1T-1]
C. [M1L0T-1]
D. [M0L0T1]
✓ Correct Answer: A.
[M0L0T-1]
Explanation:Angular velocity is angular displacement per unit time.
Explanation:Angular velocity is angular displacement per unit time.
3. Centripetal acceleration is directed towards:
A. Outside of the circle
B. Tangential direction
C. Centre of the circle
D. Upward direction
✓ Correct Answer: C. Centre of the circle
Explanation:Centripetal acceleration always acts towards the centre of the circular path.
Explanation:Centripetal acceleration always acts towards the centre of the circular path.
❓ Frequently Asked Questions
Angular displacement is the angle through which an object
rotates about a fixed axis.
The SI unit of angular velocity is radian per second (rad/s).
Centripetal acceleration is the acceleration directed towards
the centre of a circular path.