Podcast
Questions and Answers
What concept does the center of mass represent?
What concept does the center of mass represent?
- The balancing point of torques on an object (correct)
- The average mass, irrespective of distance
- The point where gravity has no effect
- The exact middle point of an object
The center of mass of an object must lie within the physical boundaries of the object.
The center of mass of an object must lie within the physical boundaries of the object.
False (B)
How does the principle of conservation of linear momentum apply to a system with no net external force?
How does the principle of conservation of linear momentum apply to a system with no net external force?
The total linear momentum remains constant
When a body explodes in mid-air, the path of the ______ continues as if no explosion occurred.
When a body explodes in mid-air, the path of the ______ continues as if no explosion occurred.
Match each scenario with the correct description of linear momentum conservation
Match each scenario with the correct description of linear momentum conservation
A system consisting of two masses, $m_1$ and $m_2$, has external forces acting on it. Under what condition is the system's total linear momentum conserved?
A system consisting of two masses, $m_1$ and $m_2$, has external forces acting on it. Under what condition is the system's total linear momentum conserved?
Impulse is a force.
Impulse is a force.
How is change in momentum related to impulse?
How is change in momentum related to impulse?
Impulse is the change in ______ of an object.
Impulse is the change in ______ of an object.
Match each item to the correct equivalent concept:
Match each item to the correct equivalent concept:
What does the 'impulse-momentum theorem' state?
What does the 'impulse-momentum theorem' state?
If a heavy truck and a soccer ball have a head-on collision, the momentum of the truck is significantly affected.
If a heavy truck and a soccer ball have a head-on collision, the momentum of the truck is significantly affected.
What is the condition for velocities after collision when the coefficient of restitution $e=1$?
What is the condition for velocities after collision when the coefficient of restitution $e=1$?
If two objects collide and stick together, the collision is considered perfectly ______.
If two objects collide and stick together, the collision is considered perfectly ______.
Match collision types with the right coefficient of restitution values:
Match collision types with the right coefficient of restitution values:
What is the nature of the force during an impact collision?
What is the nature of the force during an impact collision?
In an inelastic collision, kinetic energy is always conserved.
In an inelastic collision, kinetic energy is always conserved.
Define the term 'coefficient of restitution'.
Define the term 'coefficient of restitution'.
In a perfectly elastic collision, the coefficient of restitution (e) is equal to ______.
In a perfectly elastic collision, the coefficient of restitution (e) is equal to ______.
Match the terms used in Momentum and Collisions:
Match the terms used in Momentum and Collisions:
What remains constant after an express collision between two particles in three-dimensional isolation?
What remains constant after an express collision between two particles in three-dimensional isolation?
Linear momentum of a system is not conserved in all cases.
Linear momentum of a system is not conserved in all cases.
The rate of change of momentum is equal to what?
The rate of change of momentum is equal to what?
An ______ is a force multiplied by the time during which it acts.
An ______ is a force multiplied by the time during which it acts.
Link these types of variables
Link these types of variables
If no external forces act on a system of particles, what is conserved?
If no external forces act on a system of particles, what is conserved?
Total kinetic energy is always conserved in collisions.
Total kinetic energy is always conserved in collisions.
What provides the basis and the starting point for investigating the fundamental forces at work in particle physics?
What provides the basis and the starting point for investigating the fundamental forces at work in particle physics?
A non-zero external ______ acting on a system will cause the momentum of the system to change.
A non-zero external ______ acting on a system will cause the momentum of the system to change.
Pair values for 'e' in collisions
Pair values for 'e' in collisions
A rocket works on the principle of conservation of what physical quantity?
A rocket works on the principle of conservation of what physical quantity?
In rocket propulsion, as propellant is ejected, the mechanical energy in the rocket remains constant.
In rocket propulsion, as propellant is ejected, the mechanical energy in the rocket remains constant.
A continuous series of very small explosions generates a [blank] force on rockets.
A continuous series of very small explosions generates a [blank] force on rockets.
In rocket propulsion, the momentum gained by the rocket is equal to and opposite to the momentum of the ______.
In rocket propulsion, the momentum gained by the rocket is equal to and opposite to the momentum of the ______.
Match the scenario with the conservation principle
Match the scenario with the conservation principle
During the launch of a toy rocket, which parameter decreases as the rocket ascends?
During the launch of a toy rocket, which parameter decreases as the rocket ascends?
As fuel is expended, a rocket gains more angular momentum.
As fuel is expended, a rocket gains more angular momentum.
When can a rocket coast?
When can a rocket coast?
A rocket's acceleration is proportional to the exhaust velocity and the mass flow ______ of the gases
A rocket's acceleration is proportional to the exhaust velocity and the mass flow ______ of the gases
Flashcards
Centre of Mass (COM)
Centre of Mass (COM)
Average of masses factored by their distances from a reference.
Concept of Effective Distance
Concept of Effective Distance
Effective distance assuming total mass at the center of mass.
Center of Mass Definition
Center of Mass Definition
Point at which all mass is considered concentrated.
General COM Equation
General COM Equation
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Center of Mass (COM)
Center of Mass (COM)
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COM formula for two masses
COM formula for two masses
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Concept of the Center of Mass
Concept of the Center of Mass
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COM formula
COM formula
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Center of mass
Center of mass
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Center of Mass
Center of Mass
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Centre of Mass
Centre of Mass
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System consists
System consists
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Linear momentum
Linear momentum
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Linear Momentum
Linear Momentum
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Linear Impulse
Linear Impulse
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Impulse
Impulse
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Impulse Definition
Impulse Definition
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Impulsive tensions.
Impulsive tensions.
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Head-On Collisions
Head-On Collisions
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Oblique Collision
Oblique Collision
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Coefficient of Restitution
Coefficient of Restitution
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Impulse
Impulse
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Momentum
Momentum
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Collision String (Elastic)
Collision String (Elastic)
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Loss of KE
Loss of KE
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Rocket
Rocket
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Study Notes
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Center of Mass Definition
- Refers to the average position of all the parts of the system, weighted according to their masses
- For a two-body system, measurements from the center of mass point express a specific condition:
m1x1 = m2x2
Calculation for Multiple Particles
- The center of mass of N particles is given by
MXcm = Σ(mixi)where M is total mass - Extended to 3D:
Xcm = Σ(mixi)/M,Ycm = Σ(miyi)/M, andZcm = Σ(mizi)/M
Continuous Mass Systems
- Uses integration for calculating the center of mass
- Defined mathematically as:
Xcm = ∫xdm/M - For a non-uniform rod with linear density λ: The center of mass x is given by an integral relating the element
dmand density values
Uniform Geometric Shapes
- For a uniform rod of length L, the center of mass (CM) lies at L/2.
- A semi-circular ring features a COM at
2R/π. - A quarter circle has a COM at
2√2R / π.
Hemispherical Shell
- The center of mass for a hemi-spherical shell is at R/2 from center, when surface mass density is constant
- When surface mass density varies following σ = σ0 cos θ, the distance is
2R/3
Solid Hemisphere
- The center of mass is located as
3R/8from center on its axis of symmetry
Right Cylinder
- For a hollow cylinder, consider dm = σ(2πx sin θ)dx to find center of mass = H / 3
Remaining Mass after Scoops
- When part of an object is removed, to find center of mass fill cavity with same mass and equal mass
- Find values using given formulae
Key Equations for Momentum & Impulse
- Momentum
p=mvcan rewrite Newton's second law - Newton's second law can be expressed as
F = dp/dtwhereprepresents momentum instead ofF=ma - Law of conservation of momentum
p = constant - Impulse is integral of force over time, leads to change in momentum.
Impulse Equation
- Defined as
I = ∫F dt - For variable mass systems following a rocket propulsion
- Thrust force
Ft = Vrel dm/dtwhere Vrel relative velocity
Important Rocket Propulsion Formulas
- Force equation can be written as F = V dm / dt
- Standard rocket equation is Vf = V0 + C ln (𝑚0/𝑚f) with C = gas constant.
Key Equations
- For linked objects
Mxcm = Σ Mixiin system - Law of conservation of momentum
- Law of Kinematics: v = u + gt ; v2 = u2 + 2as; s = ut + 1 /2 at2
Collisions
- Collisions explained at a high level
- Discuss equation for elastic and inelastic collisions
- e = 1 for highly elastic collisions
- e = 0 for highly inelastic collisions
Coefficient of Restitution
- Defines the nature of a collision
- Represented as
e = (separation velocity) / (approach speed) - Where values range from 0 (perfectly inelastic) to 1 (perfectly elastic)
Loss of Kinetic Energy
- With a loss of kinetic energy with collision the loss is calculated by relating initial conditions to variables
Common Tangent
- The velocities of components along a common tangent remains same but along the line gets impact direction change
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