Angular Acceleration Last Updated : 04 Feb, 2024 Comments Improve Suggest changes Like Article Like Report Angular acceleration is the change in angular speed per unit of time. It can also be defined as the rate of change of angular acceleration. It is represented by the Greek letter alpha (α). The SI unit for the measurement of, Angular Acceleration is radians per second squared (rad/s2). In this article, we will learn about Angular Acceleration and its formula in detail. What Is Angular Acceleration?For an object in a circular motion, angular velocity varies with time and this change in angular velocity is called angular acceleration. It is a vector quantity that has both magnitude and direction and is also known as rotational acceleration. It can be interpreted as the time rate of change in the angular velocity. The image given below tells us about angular acceleration. Angular Acceleration is usually expressed in radians per second whole square. Thus, α = dω / dt Angular acceleration is also known as rotational acceleration. Angular Acceleration is a pseudoscalar quantity. It is considered positive if the angular speed increases counterclockwise and is considered negative if the angular speed increases clockwise. Examples of Angular Acceleration include the motion of the wheel, fan, earth, etc. Angular Acceleration UnitThe direction of the angular acceleration is always perpendicular to the plane of rotation. When the object rotates clockwise, then the angular acceleration points away from the observer, if the object rotates counterclockwise, then the vector of angular acceleration points toward the viewer. SI unit of angular acceleration is (rad/s2) and is usually denoted by the alpha (α).  Its dimensional formula is given by [M0L1 T-2]. Angular Acceleration Formulaα = dω/dt where,α is the angular accelerationω is the angular velocityt is the time taken by the object If angular displacement θ is given then the angular acceleration is calculated as, α = d2θ/dt2 DerivationSuppose an object is doing circular motion with a linear velocity v, angular velocity ω on a circular path of radius r in time t. Now, we know the angular acceleration of an object is the first derivative of its angular velocity with respect to time. So we get, α = dω/dt  ....... (1) Also we know that the angular velocity of an object is the first derivative of its radius with respect to time. ω = dθ/dt  ....... (2) Substituting (2) in (1) we get, α = d(dθ/dt)/dt α = d2θ/dt2 This derives the formula for angular acceleration. How is Angular Acceleration Determined?Angular acceleration is the rate at which the angular speed changes with respect to the time taken of a rotating object. Angular acceleration is a pseudovector quantity. that focuses on a path along with the turning pivot. Its unit is radians/s2 and is calculated by the equation discussed below, α = dω/dt α = ω2 - ω1 / t2 - t1 where,ω2 is the final velocityω1 is the initial velocityt1 is initial timet2 is finial time What Causes Angular Acceleration?If an object is pivoted at one endpoint and a force is applied on the other endpoint, then this applied force tends to rotate the object and is called torque. The torque applied on the body is directly proportional to the angular acceleration of the object, i.e. the more torque is applied the more the angular acceleration of the object. This torque is the very reason that rotates a body. A body performing circular motion has an angular velocity if the angular velocity is constant then the object is in Uniform Circular Motion. Also, Check Circular VelocityDynamics of Circular MotionMotion in a Vertical CircleSolved Examples on Angular AccelerationExample 1: Calculate the angular acceleration of an object if its angular velocity changes at the rate of 50 rad/s for 5 seconds. Solution: dω = 50 dt = 5 Using the formula we have, α = dω/dt  = 50/5  = 10 rad/s2 Example 2: Calculate the angular acceleration of an object if its angular velocity changes at the rate of 90 rad/s for 4 seconds. Solution: dω = 90 dt = 4 Using the formula we have, α = dω/dt  = 90/4  = 22.5 rad/s2 Example 3: Calculate the angular velocity of an object if its angular acceleration is 30 rad/s2 for 7 seconds. Solution: α = 30 dt = 7 Using the formula we have, α = dω/dt dω = α dt dω = 30 (7) dω = 210 rad/s Example 4: Calculate the angular velocity of an object if its angular acceleration is 16 rad/s2 for 3 seconds. Solution: α = 16 dt = 3 Using the formula we have, α = dω/dt dω = α dt dω = 16 (3) dω = 48 rad/s Example 5: Calculate the time taken by an object if its angular velocity is 46 rad/s and acceleration is 23 rad/s2. Solution: α = 23 dω = 46 Using the formula we have, α = dω/dt dt = dω/α dt = 46/23 dt = 2 s Example 6. Calculate the angular acceleration of an object if its angular displacement is 60 radians and its time is 12 seconds. Solution: dθ = 60 dt = 12 Calculate the angular velocity of the object. ω = dθ/dt ω = 60/12 ω = 5 rad/s Using the formula we have, α = dω/dt  = 5/12  = 0.416 rad/s2 Example 7: Calculate the angular acceleration of an object if its angular displacement is 45 radians and its time is 3 seconds. Solution: dθ = 45 dt = 3 Calculate the angular velocity of the object. ω = dθ/dt ω = 45/3 ω = 15 rad/s Using the formula we have, α = dω/dt  = 15/3  = 5 rad/s2 Comment More infoAdvertise with us Next Article Torque and Angular Momentum P prabhjotkushparmar Follow Improve Article Tags : School Learning Physics Physics-MAQ Physics-Formulas Mechanics Physics-Concepts +2 More Similar Reads CBSE Class 11 Physics Notes CBSE Class 11 Physics Notes 2023-24 is a comprehensive guide for CBSE Class 11 students. The class 11 syllabus is designed to provide students with a strong foundation in the basic principles of physics, including Measurement, Vectors, Kinematics, Dynamics, Rotational Motion, Laws of Motion, and Gra 12 min read Chapter 1 - UNITS AND MEASUREMENTMeasurementMeasurement is the process of finding out how much, how big, or how heavy something is. It’s like a way to compare things using a standard unit. For example:How long? 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