Physics Lesson 7.1.3 - Uniformly Accelerated (Decelerated) Rotational Motion

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Welcome to our Physics lesson on Uniformly Accelerated (Decelerated) Rotational Motion, this is the third lesson of our suite of physics lessons covering the topic of Kinematics of Rotational Motion, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Uniformly Accelerated (Decelerated) Rotational Motion

Again, we can use the analogy between the linear and circular motion to explain the uniformly accelerated (decelerated) motion, which in itself is part of non-uniform circular motion which we will not discuss here as it is very complicated for the level required in this webpage.

As examples of uniformly accelerated rotational motion we can mention objects that start rotating from rest. Their rotation accelerates until they reach a steady rate. Only then, the rotational motion can be considered as uniform. On the other hand, when a rotation is slowing down until it stops (wheels when a car is slowing down, drum of a washing machine when you turn the power off, etc), we have a uniformly decelerated rotational motion.

a. Initial and final angular velocity

Just as in linear motion, we have an initial and final angular velocity, whose values are not equal. We can write ω0 for the initial and ω for the final angular velocity of a rotating object.

b. Angular acceleration

It is obvious that the change in angular velocity mentioned above, takes a certain time to occur. Hence, we can speak here for a kind of acceleration, known as angular acceleration and is denoted by the symbol alpha (α). From the analogy with linear motion it is very easy to write its formula.

α = ∆ω/t = ω - ω0/t

The unit of angular acceleration obviously is [rad/s2] as angular velocity is measured in [rad/s] and the time in [s].

The abovementioned analogy can be extended for the other three equations of uniformly accelerated (deceleration) motion of both types. The following table includes all these formuleae.

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(L is used here to represent the linear distance instead of s, in order to fit the topic discussed here).

Example 3

A platform starts rotating from rest and after 12 s it reaches an angular velocity of 24 rad/s. The platform radius is 4 m and a small object is attached at the edge of platform as shown in the figure.

Physics Tutorials: This image provides visual information for the physics tutorial Kinematics of Rotational Motion
Calculate:
  1. Angular displacement of the object
  2. Angular acceleration of the platform
  3. Total distance travelled by the object

Solution 3

a. From the equation

φ = (ω + ω0) × t/2

and giving that ω0 = 0, ω = 24 rad/s and t = 12 s, we obtain for the angular displacement

φ = (0 + 24) × 12/2
= 24 × 12/2
= 144 rad

b. Angular acceleration is calculated by the first equation or rotational accelerated motion written in terms of α, as

α = ω - ω0/t

Substituting the values, we obtain

α = 24 - 0/12
= 2 rad/s2

c. Distance L is calculated by the equation

L = φ × r

where r = 4 m is the radius of the platform. Therefore, we obtain

L = 144 × 4
= 576 m

You have reached the end of Physics lesson 7.1.3 Uniformly Accelerated (Decelerated) Rotational Motion. There are 4 lessons in this physics tutorial covering Kinematics of Rotational Motion, you can access all the lessons from this tutorial below.

More Kinematics of Rotational Motion Lessons and Learning Resources

Rotation Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
7.1Kinematics of Rotational Motion
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
7.1.1Understanding Some Useful Quantities of Rotational Motion as a Background
7.1.2Kinematics of Uniform Circular Motion
7.1.3Uniformly Accelerated (Decelerated) Rotational Motion
7.1.4The Meaning of Centripetal Acceleration

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