Angular Acceleration

Angular Acceleration: Meaning, Formula, Examples & FAQs

Angular acceleration is a key concept in rotational motion, representing the rate of change of angular velocity with respect to time. Learn its definition, formulas, SI unit, derivations, solved examples, FAQs, and MCQs—everything you need for exams or understanding rotational dynamics in physics.

What Is Angular Acceleration?

Angular acceleration (α) is defined as the rate at which an object's angular velocity changes with time. It is a vector quantity, measured in radians per second squared (rad/s²). Angular acceleration describes how quickly a rotating object speeds up or slows down.

Angular Acceleration: Formulas Sheet

Average Angular Acceleration:
α = (ω_final − ω_initial)/t
Instantaneous Angular Acceleration:
α = dω/dt
Relation to Linear Acceleration:
a = rα (where r = radius)
Rotational Equations (constant α):
- ω = ω₀ + αt
- θ = ω₀t + ½αt²
- ω² = ω₀² + 2α(θ−θ₀)
Torque-Angular Acceleration:
τ = Iα
(where τ is torque, I is moment of inertia)

SI Unit and Vector Direction

SI Unit: radians per second squared (rad/s²)
Vector Direction: Perpendicular to the plane of rotation. Positive α = counterclockwise; Negative α = clockwise.

Angular Acceleration: Solved Examples

Example 1: A disc's angular velocity increases from 0 to 60 rad/s in 10 s. Find the angular acceleration.
Solution: α = (ω_final – ω_initial)/t = (60 – 0)/10 = 6 rad/s²
Example 2: A flywheel starts from rest and reaches 100 rad/s in 20 s. What is its angular acceleration?
Solution: α = (100 – 0)/20 = 5 rad/s²
Example 3 (Torque): A wheel with I = 2 kg·m² experiences a torque of 10 Nm. Find α.
Solution: α = τ/I = 10/2 = 5 rad/s²

Practice MCQs: Angular Acceleration

If a fan's angular velocity increases from 10 rad/s to 50 rad/s in 4 seconds, what is the angular acceleration?
A) 10 rad/s² B) 20 rad/s² C) 5 rad/s² D) 40 rad/s²
Answer: C) 10 rad/s²
What is the SI unit of angular acceleration?
A) m/s B) rad/s² C) rad/s D) m/s²
Answer: B) rad/s²
If the torque acting on a wheel is doubled (I constant), what happens to the angular acceleration?
A) Doubled B) Halved C) Unchanged D) Zero
Answer: A) Doubled
If angular velocity remains constant, angular acceleration is:
A) Maximum B) Zero C) Negative D) Cannot be determined
Answer: B) Zero
Angular acceleration is a ________ quantity.
A) Scalar B) Vector C) Pseudoscalar D) Both B and C
Answer: D) Both B and C

Frequently Asked Questions (FAQs) on Angular Acceleration

What is angular acceleration in simple terms?
It is the rate at which the angular velocity of a rotating object changes with time.
What is the formula for angular acceleration?
α = (ω_final – ω_initial)/t or α = dω/dt
What are some real-life examples of angular acceleration?
Rotating wheels, spinning fans, earth’s rotation changes, the motion of a merry-go-round, acceleration of a bicycle’s wheel.
What is the difference between angular acceleration and linear acceleration?
Linear acceleration refers to change in straight-line speed, while angular acceleration refers to change in rotational speed.
What is the relationship between torque and angular acceleration?
Torque (τ) = moment of inertia (I) × angular acceleration (α). More torque means more angular acceleration for the same object.
Can angular acceleration be negative?
Yes. Negative α means the object is slowing down or the direction is clockwise (based on convention).
How is angular acceleration used in engineering?
It is used to design gears, engines, turbines, and analyze the motion of rotating machinery.
How do you measure angular acceleration?
It can be measured using angular velocity sensors, gyroscopes, or by calculation from rotational motion data.
Does angular acceleration affect centripetal force?
Yes, if angular acceleration changes angular velocity, centripetal force will also change (F = mω²r).
Why is angular acceleration important in physics?
It is key to understanding rotational dynamics, predicting motion of rotating bodies, and engineering systems.