Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Q.1 : Write one of difference between Rotational and translational motion.
Ans. In translational motion of the rigid body all particles of the rigid body have same linear displacement, same linear velocity and same linear acceleration while in Rotational motion, When a rigid object rotates, points on the object, such as A, B, or C. move in circular paths. An imaginary line perpendicular to plane of circular paths of particles of a rigid body in rotation and containing the centers of all these circular paths is known as axis of rotation.
Q.2 : Write one example of Rotational motion about a fixed axis.
Ans. Ceiling fan rotation
Q.3 : Write one example of Rotational motion about an axis which is not fixed
Ans. Motion of ball rolling down an incline plane.
Dynamics Of Rotational Motion, Rotation About A Fixed Axis, Important Topics For JEE 2025
Dynamics Of Rotational Motion : Discover the fascinating world of rotational motion in physics. This guide covers key concepts such as angular velocity, torque, moment of inertia, and the laws governing rotational dynamics. Learn how forces cause rotational motion and explore practical applications in everyday life, from spinning wheels to celestial bodies.
Shrivastav 21 May, 2024
Share
Dynamics Of Rotational Motion :
A rigid body is defined as an object that has fixed size and shape. In other words, the relative positions of its constituent particles remain constant. In actual, a rigid body does not exist – it is a useful idealization. By the term
fixed axis
, we mean that the axis must be fixed relative to the body and fixed in direction relative to an inertial position.
A rigid body may have either of the following three types of motions :
(i)
Translational motion
(ii)
Rotational motion
(iii)
Translational plus rotational motion
In translational motion of the rigid body all particles of the rigid body have same linear displacement, same linear velocity and same linear acceleration. In rest two motions, different particles have different linear displacement, different linear velocity and different linear acceleration.
As far as translational motion is concerned we do not differentiate between a particle and a rigid body.
This motion is already discussed in the chapter of kinematics. This is the reason, in the chapter of kinematics, sometimes we write: a particle is moving and sometimes we write: a block (or a body) is moving. Rest two motions are only defined for a rigid body.
Dynamics Of Rotational Motion
A rigid body may have either of the following three types of motions :
(i)
Translational motion
(ii)
Rotational motion
(iii)
Translational plus rotational motion
In translational motion of the rigid body all particles of the rigid body have same linear displacement, same linear velocity and same linear acceleration. In rest two motions, different particles have different linear displacement, different linear velocity and different linear acceleration.
As far as translational motion is concerned we do not differentiate between a particle and a rigid body.
This motion is already discussed in the chapter of kinematics. This is the reason, in the chapter of kinematics, sometimes we write: a particle is moving and sometimes we write: a block (or a body) is moving. Rest two motions are only defined for a rigid body. In the present chapter, we shall discuss these two motions of a rigid body.
Types Of Rotational Motion
Motion of body involving rotation can be classified into the following two categories.
(i)
Rotation about a fixed axis or pure rotation.
(ii)
Rotation about an axis in translation or combined rotation and translation
Rotation About A Fixed Axis Or Pure Rotation
When a rigid object rotates, points on the object, such as
A
,
B
, or
C
. move in circular paths. An imaginary line perpendicular to plane of circular paths of particles of a rigid body in rotation and containing the centers of all these circular paths is known as axis of rotation. Rotation of ceiling fan, potter's wheel, opening and closing of doors and hands of a wall clock etc. come into this category.
Combined Rotation And Translation
Combined Rotation And Translation :
The most general motion of a rigid body is the combination of translational and rotational motions. We have studied pure rotation and pure translation motions but what happens when the two are combined? The most familiar example of combined rotational and translational motion is a rolling wheel. Consider rolling of wheels of a vehicle, moving on straight level road. Relative to a reference frame the axel fixed with the vehicle, the wheel appears rotating about its axel. The rotation of the wheel from this frame is pure rotation about fixed axis. But relative to a reference frame fixed with the ground, the wheel appears rotating about the moving axel, therefore, rolling of a wheel is superposition of two simultaneous but distinct motions-rotation about the fixed axel and translation of the wheel along the level road.
Rotation Of A Rigid Body About A Fixed Axis
When a body is rotating about a fixed axis, any point
P
located in the body travels along a circular path. Before, analyzing the circular motion of point
P
, we will first study the angular motion properties of a rigid body.
Angular Motion :
Since, a point is without dimension, it has no angular motion. Only lines or bodies undergo angular motion. Let us consider the angular motion of a radial line
r
located with the shaded plane.
Angular Position :
∙
The angular position of
r
is defined by the angle θ, measured between a fixed reference line
OA
and
r
.
Angular Displacement :
The change in the angular position, often measured as a differential
d
θ is called the angular displacement. (Finite angular displacements are not vector quantities, although differential rotations
d
θ are vectors). This vector has a magnitude
d
θ and the direction of
d
θ is along the axis.
Specifically, the direction of
d
θ is determined by right hand rule; that is, the fingers of the right hand are curled with the sense of rotation, so that in this case the thumb or
d
θ points upward.
Angular Velocity In Rotational Motion
Angular Velocity :
The time rate of change in the angular position is called the angular velocity
. Thus,
It is expressed here in scalar form, since its direction is always along the axis of rotation, i.e., in the same direction as
Angular Acceleration In Rotational Motion
Angular Acceleration :
∙
The angular acceleration α measures the time rate of change of the angular velocity. Hence, the magnitude of this vector may be written as,
∙
It is also possible to express α as,
Instantaneous axis of rotation
In combined translational and rotational motion, we cannot have a permanent axis of rotation. However, there may be a point inside the given body (or extended body) which can be momentarily at rest. This is what we call instantaneous axis of rotation.
Consider a rod which remains always in the same vertical plane with its ends in contact with smooth wall and floor as shown in figure. As the rod slides, its centre of mass translates and the rod rotates about a horizontal axis passing through centre of mass. The motion of such an object can be analyzed by making equations for translation and rotation separately, which involves lengthy calculations.
Torque And Angular Acceleration For A Rigid Body
The angular acceleration of a rigid body is directly proportional to the sum of the torque components along the axis of rotation. The proportionality constant is the inverse of the moment of inertia about that axis, or
The angular acceleration of a rigid body is directly proportional to the sum of the torque components along the axis of rotation. The proportionality constant is the inverse of the moment of inertia about that axis, or
Thus, for a rigid body we have the rotational analog of Newton’s second law:
…(iii)
Following two points are important regarding the above equations:
(i)
The above equation is valid only for rigid bodies. If the body is not rigid like a rotating tank of water, the angular acceleration
is different for different particles.
(ii)
The sum
in the above equation includes only the torques of the external forces, because all the internal torques add to zero.
Torque And Angular Acceleration For A Rigid Body
Table given ahead compares the linear and angular motion with constant acceleration.
Straight line motion with constant linear acceleration
Fixed axis rotation with constant angular acceleration
a
= constant
= constant
v
=
u
+
at
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
