1. Rotational Dynamics ❖ Characteristics of Circular Motion
❖ Definition:
“Motion of object along the circular path or
circumference of circle is called as circular
motion.”
• Example of circular motion:
i) Motion of blade of fan. ❖ Kinematics of Circular Motion:
ii) Motion of tip on the hand of clock.
iii) Motion of planate around the sun. Angular Displacement
The angle which is subtended by the
position vector at the centre of the
circular path refers to the angular
displacement.
Angular Displacement
• Radius Vector: 𝜟𝑺
Δθ =
A vector drawn from center of circle to 𝒓
the position of particle on circumference
is called as radius vector. Where,
Δs- refers to the linear displacement
• Radius vector is vector quantity and r- is the radius.
Magnitude of radius vector is same but Radian is the unit of Angular Displacement.
direction varies at every point.
• SI unit: meter (m)
• CGS: centimeter (cm)
• Dimension Formula: [L1]
• Direction of angular displacement is
perpendicular to the plane of motion.
For one complete rotation total angular
displacement is 2𝜋 𝑐 𝑜𝑟 3600
, ❖ Angular And Linear Velocity
❖ Relation between Linear and Angular
velocity:
❖ Right Hand thumb Rule:
• Imagine the axis of rotation to be held in
right hand with the fingers curled
around it and thumb out-stretched.
• If the curled fingers give the direction of
motion of a particle performing circular
motion, then the direction of out-
stretched thumb gives the direction of
angular displacement vector.
, • Angular acceleration is vector quantity.
Direction of angular acceleration is
depended on (angular velocity). The
direction of 𝛼 is along the axis of rotation.
• If (𝝎
⃗⃗⃗ ) is increasing then the direction of 𝜶
⃗⃗
is same as the direction of 𝝎 ⃗⃗⃗ .
• If (𝜔
⃗ ) is decreasing then the direction of 𝜶
⃗⃗
⃗⃗⃗⃗⃗ .
is opposite is the direction of (𝝎)
• For a uniform circular motion angular
acceleration is zero.
• The direction of angular acceleration for ❖ Uniform circular motion (UCM):
non-uniform circular motion is
perpendicular to the plane of i. During circular motion if the speed of
motion and its direction is depend on the the particle remains constant, it is called
magnitude of (𝝎⃗⃗⃗ ). Uniform Circular Motion (UCM).
❖ Angular And Linear Accelerations:
❖ Definition:
“Motion of object along the circular path or
circumference of circle is called as circular
motion.”
• Example of circular motion:
i) Motion of blade of fan. ❖ Kinematics of Circular Motion:
ii) Motion of tip on the hand of clock.
iii) Motion of planate around the sun. Angular Displacement
The angle which is subtended by the
position vector at the centre of the
circular path refers to the angular
displacement.
Angular Displacement
• Radius Vector: 𝜟𝑺
Δθ =
A vector drawn from center of circle to 𝒓
the position of particle on circumference
is called as radius vector. Where,
Δs- refers to the linear displacement
• Radius vector is vector quantity and r- is the radius.
Magnitude of radius vector is same but Radian is the unit of Angular Displacement.
direction varies at every point.
• SI unit: meter (m)
• CGS: centimeter (cm)
• Dimension Formula: [L1]
• Direction of angular displacement is
perpendicular to the plane of motion.
For one complete rotation total angular
displacement is 2𝜋 𝑐 𝑜𝑟 3600
, ❖ Angular And Linear Velocity
❖ Relation between Linear and Angular
velocity:
❖ Right Hand thumb Rule:
• Imagine the axis of rotation to be held in
right hand with the fingers curled
around it and thumb out-stretched.
• If the curled fingers give the direction of
motion of a particle performing circular
motion, then the direction of out-
stretched thumb gives the direction of
angular displacement vector.
, • Angular acceleration is vector quantity.
Direction of angular acceleration is
depended on (angular velocity). The
direction of 𝛼 is along the axis of rotation.
• If (𝝎
⃗⃗⃗ ) is increasing then the direction of 𝜶
⃗⃗
is same as the direction of 𝝎 ⃗⃗⃗ .
• If (𝜔
⃗ ) is decreasing then the direction of 𝜶
⃗⃗
⃗⃗⃗⃗⃗ .
is opposite is the direction of (𝝎)
• For a uniform circular motion angular
acceleration is zero.
• The direction of angular acceleration for ❖ Uniform circular motion (UCM):
non-uniform circular motion is
perpendicular to the plane of i. During circular motion if the speed of
motion and its direction is depend on the the particle remains constant, it is called
magnitude of (𝝎⃗⃗⃗ ). Uniform Circular Motion (UCM).
❖ Angular And Linear Accelerations:
