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XI Phy New Chap 06 System of_Particles_&_Rotational_Motion_106_A&R.
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Spread the Happiness. Assertion and Reason Statements Feedback: 9008271516XII_Phy_New_Chap-02 _ ELECTROSTATIC POTENTIAL AND CAPACITANCE
S# Correct Assertion Correct Reason
6.1 INTRODUCTION
The particle model is inadequate for extended Extended bodies have finite size and rotational motion,
1
bodies. not captured by a point-like mass.
The center of mass (COM) is a crucial concept It simplifies analysis by representing the entire system's
2 for analyzing extended bodies. motion as a single point considering mass distribution.
A rigid body is an idealized model for analyzing It assumes a fixed shape with constant particle distances,
3 extended bodies. simplifying analysis despite real-world deformations.
Pure translational motion involves all parts of a This ensures the body maintains its relative shape during
4 rigid body moving with the same velocity at any motion (e.g., sliding block).
instant.
Rotational motion involves particles following This defines a specific type of motion relative to a
5
circular paths around a fixed axis. stationary axis (e.g., ceiling fan).
Rolling motion combines both translation and Different particles undergo a change in position
6 rotation. (translation) and orientation (rotation) (e.g., rolling
cylinder).
Fixed-axis rotation is simpler to analyze than The stable reference point of a fixed axis simplifies the
7
moving-axis rotation. study of rotational dynamics.
6.2 CENTRE OF MASS
Center of mass (CoM) is the system's mass Establishes CoM as a reference for mass distribution.
8
distribution average location.
CoM position for two particles depends on their Formula relates CoM location to particle properties for
9
masses and distances. calculation.
CoM for multiple particles on a line is a Extends CoM concept to multiple particles, providing a
10
weighted sum of positions and masses. general formula.
Coordinates and masses define CoM location Enables CoM analysis for particles in two dimensions.
11
for any 2D particle arrangement.
Vector notation and summation establish 3D Provides a comprehensive framework for CoM
12
CoM position for any distribution. determination in three dimensions.
Integrals handle continuous mass distributions, Transitions from discrete particles to continuous mass for
14
extending CoM applicability. broader use.
Symmetry simplifies CoM determination in Reduces complex calculations by leveraging symmetry
15
homogeneous shapes (rings, discs). properties.
Reflection symmetry makes a thin rod's CoM Defines the relationship between symmetry and CoM
16
coincide with its geometric center. location in rods.
An equilateral triangle's centroid is its CoM, Identifies equivalence between centroid and CoM for
17
demonstrating a practical application. specific geometries.
Lamina examples showcase CoM determination Highlights the versatility of CoM concepts for diverse
18 in complex shapes using symmetry and geometries.
geometry.
CoM reflects a system's mass distribution, Links CoM to motion characteristics for a concise
19
influencing its motion. definition.
Mass-weighted averages pinpoint the CoM Quantifies CoM position relative to individual particles for
20
relative to particles. precise calculation.
For equal-mass particles, the CoM coincides Demonstrates the geometric relationship between CoM
21
with the centroid (e.g., equilateral triangle). and centroid under specific conditions.
Symmetry considerations simplify CoM Explains how symmetry offers a practical approach for
22 determination in regular, homogeneous shapes. CoM in these bodies.
Reflection symmetry positions a thin rod's CoM Establishes a direct link between symmetry and CoM
23
at its geometric center. location in rods.
Mass distribution at geometric centers Demonstrates a systematic method for CoM calculation
24 determines the CoM in uniform, regular shapes using uniformity and regularity.
(e.g., L-shaped lamina).
6.3 MOTION OF CENTRE OF MASS
External forces govern the motion of a system's Internal forces cancel out due to Newton's third law,
25 center of mass. leaving only external forces to influence the center of
mass motion.
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, Spread the Happiness. Assertion and Reason Statements Feedback: 9008271516
XII_Phy_New_Chap-02 _ ELECTROSTATIC POTENTIAL AND CAPACITANCE
S# Correct Assertion Correct Reason
The center of mass motion signifies a system's By definition, the center of mass represents the weighted
26 overall translational motion. average position of all particles, reflecting their net linear
movement.
A projectile's center of mass maintains its Cancelling internal explosive forces leaves the external
27 parabolic trajectory despite an internal gravity acting before and after the explosion, resulting in
explosion. the unchanged motion of the center of mass.
Analyzing the center of mass motion isolates By treating a rigid body as a system of particles, focusing
the linear motion of a rigid body from its on the center of mass separates its translational motion
28
rotation. independent of any rotational aspects.
The product of a system's mass and its center This relationship, derived from Newton's second law,
29 of mass acceleration equals the vector sum of applies to the center of mass, treating the system's mass
all external forces acting on it. as concentrated there.
The concept of the center of mass simplifies By isolating the center of mass motion (translation) from
analyzing a rigid body's motion by separating the overall motion, we can analyze each component
30
translational and rotational components. independently, leading to a clearer understanding.
6.4 LINEAR MOMENTUM OF A SYSTEM OFPARTICLES
Zero net external force on a system leads to Canceling external forces results in constant total
31
conserved total linear momentum. momentum.
Center of mass motion reflects the system's The total momentum of a system equals the product of its
32
overall linear motion. total mass and the center of mass velocity.
Radioactive decay maintains the center of mass Negligible external forces during decay ensure conserved
motion. total momentum. Emitted particles strategically move to
33
keep the center of mass on its original path.
Analyzing center of mass motion simplifies Separating the center of mass motion (translation) from
34 complex system motions. individual particle motions clarifies the overall picture
(easier analysis).
A binary star system's center of mass traces a No external forces imply constant total momentum,
35 straight line in the absence of external forces. causing the center of mass to move uniformly in a straight
line.
In the center of mass frame, resultant particles Conservation of total momentum in the center of mass
36 from a split move back-to-back. frame requires particles to move in opposite directions
(zero net momentum).
Internal forces can cause complex particle While the center of mass moves uniformly (zero net
37 motions despite constant center of mass external force), internal interactions between particles can
motion. lead to intricate individual particle trajectories.
Center of mass frame simplifies analysis of In the center of mass frame, the center of mass remains at
particle motion after a split. rest after a split, whereas the laboratory frame shows
38
particles moving back-to-back, offering a clearer view of
particle interactions.
6.5 VECTOR PRODUCT OF TWO VECTORS
Vector product of two vectors results in a Notation uses "x" symbol.
39
vector, also called "cross product".
Magnitude of the vector product depends on the Represented by c =
40 angle and magnitudes of the two initial vectors.
Vector product is perpendicular to the plane Ensures rotational effect and aligns with the right-hand
41
containing the two initial vectors. screw rule.
Vector product differs from scalar product. Not commutative (a x b ≠ b x a) and results in a vector,
42
unlike scalar product which is a scalar.
Right-hand screw rule determines the direction Rotating the screw from tail (a) to head (b) gives the
43
of the vector product. perpendicular vector (c).
Vector product is essential for calculating Plays a fundamental role in analyzing rotational motion.
44
moment of force and angular momentum.
6.6 ANGULAR VELOCITY AND ITS RELATION WITH LINEAR VELOCITY
In rotational motion about a fixed axis, a particle Introduces the concept of a central axis of rotation (fixed
45 traces a circle. axis) around which particles travel in circular paths due to
their constant distance from it.
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