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System of particle & Rigid body PPT Physics Class 11

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SYSTEM OF 
PARTICLES 
AND 
ROTATIONAL 
MOTION
Page 2


SYSTEM OF 
PARTICLES 
AND 
ROTATIONAL 
MOTION
Definitions of 
some special 
terms
• 1. Angular position (F) - The angular 
position of a particle is the angle ? 
made between the line connecting the 
particle to the original and the positive 
direction of the x-axis, measured in a 
counterclockwise direction.
• . Angular displacement (?) - The radian 
value of the angle displaced by an 
object on the center of its path in 
circular motion from the initial position 
to the final position is called the angular 
displacement.
Page 3


SYSTEM OF 
PARTICLES 
AND 
ROTATIONAL 
MOTION
Definitions of 
some special 
terms
• 1. Angular position (F) - The angular 
position of a particle is the angle ? 
made between the line connecting the 
particle to the original and the positive 
direction of the x-axis, measured in a 
counterclockwise direction.
• . Angular displacement (?) - The radian 
value of the angle displaced by an 
object on the center of its path in 
circular motion from the initial position 
to the final position is called the angular 
displacement.
*Angular acceleration- Angular acceleration 
of an object in
circular motion is the rate of change of 
angular velocity
Unit- rads^-2
Direction- By right hand rule
*Angular Velocity (?)- Angular velocity of an 
object in circular
motion is the rate of change of angular 
displacement
? = ? / t
Unit – rads^-1
Vector direction by
Right hand rule
Page 4


SYSTEM OF 
PARTICLES 
AND 
ROTATIONAL 
MOTION
Definitions of 
some special 
terms
• 1. Angular position (F) - The angular 
position of a particle is the angle ? 
made between the line connecting the 
particle to the original and the positive 
direction of the x-axis, measured in a 
counterclockwise direction.
• . Angular displacement (?) - The radian 
value of the angle displaced by an 
object on the center of its path in 
circular motion from the initial position 
to the final position is called the angular 
displacement.
*Angular acceleration- Angular acceleration 
of an object in
circular motion is the rate of change of 
angular velocity
Unit- rads^-2
Direction- By right hand rule
*Angular Velocity (?)- Angular velocity of an 
object in circular
motion is the rate of change of angular 
displacement
? = ? / t
Unit – rads^-1
Vector direction by
Right hand rule
Angular 
equations 
of 
movemen
t
1. ? = ?0 + at
2. ? = (? + ?0 )t/2
3. ? = ?0t + ½ at^2
4. ?2 = ?0^2 + 2a?
Page 5


SYSTEM OF 
PARTICLES 
AND 
ROTATIONAL 
MOTION
Definitions of 
some special 
terms
• 1. Angular position (F) - The angular 
position of a particle is the angle ? 
made between the line connecting the 
particle to the original and the positive 
direction of the x-axis, measured in a 
counterclockwise direction.
• . Angular displacement (?) - The radian 
value of the angle displaced by an 
object on the center of its path in 
circular motion from the initial position 
to the final position is called the angular 
displacement.
*Angular acceleration- Angular acceleration 
of an object in
circular motion is the rate of change of 
angular velocity
Unit- rads^-2
Direction- By right hand rule
*Angular Velocity (?)- Angular velocity of an 
object in circular
motion is the rate of change of angular 
displacement
? = ? / t
Unit – rads^-1
Vector direction by
Right hand rule
Angular 
equations 
of 
movemen
t
1. ? = ?0 + at
2. ? = (? + ?0 )t/2
3. ? = ?0t + ½ at^2
4. ?2 = ?0^2 + 2a?
MOTION
TRANSLATION
COMBINATION OF 
TRANSLATION AND 
ROTATION
ROTATION
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FAQs on System of particle & Rigid body PPT Physics Class 11

1. What is the difference between translational motion and rotational motion in a system of particles?
Ans.Translational motion refers to the movement of an entire system of particles from one location to another, where all particles move in the same direction and with the same velocity. In contrast, rotational motion involves the movement of particles around a central axis, where different particles may have different velocities depending on their distance from the axis of rotation.
2. How do we calculate the center of mass for a system of particles?
Ans.The center of mass (COM) for a system of particles is calculated using the formula: \[ \text{COM} = \frac{\sum m_i \cdot r_i}{\sum m_i} \] where \( m_i \) represents the mass of each particle and \( r_i \) is the position vector of each particle. The center of mass is the average position of all the masses in the system, weighted by their respective masses.
3. What are the main equations of motion for rotational dynamics?
Ans.The main equations of motion for rotational dynamics are analogous to linear motion equations. They include: 1. \( \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 \) (angular displacement) 2. \( \omega = \omega_0 + \alpha t \) (angular velocity) 3. \( \omega^2 = \omega_0^2 + 2\alpha \theta \) (angular acceleration) where \( \theta \) is the angular displacement, \( \omega \) is the angular velocity, \( \alpha \) is the angular acceleration, and \( t \) is time.
4. What role does the moment of inertia play in rotational motion?
Ans.The moment of inertia is a measure of an object's resistance to changes in its rotational motion about an axis. It depends on the mass distribution of the object relative to the axis of rotation. The greater the moment of inertia, the harder it is to change the rotational state of the object, which is represented mathematically in Newton's second law for rotation as: \[ \tau = I \alpha \] where \( \tau \) is the torque, \( I \) is the moment of inertia, and \( \alpha \) is the angular acceleration.
5. How is torque related to angular momentum in a system of particles?
Ans.Torque is the rate of change of angular momentum in a system of particles. This relationship is expressed mathematically by the equation: \[ \tau = \frac{dL}{dt} \] where \( \tau \) is the torque and \( L \) is the angular momentum. This indicates that if a net torque acts on a system, it will result in a change in its angular momentum over time.
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