PHY 101: General Physics 1 Key Concepts
Page 1
PHYSICS: Study of nature and properties of matter and energy including heat, light, sound, electricity, and magnetism.
Page 2
Course Outline Topics:
Space and time
Units and dimensions
Vectors and scalars
Kinematics
Newton’s Laws of motion
Conservation principles
Rotational motion
Gravitation
Page 3
Measurement: Process of comparing an unknown physical quantity with a known fixed physical quantity (e.g., unit). Units should be well-defined and reproducible.
Standard Units:
Fundaments units: Length, mass, time, and others.
Derived units: Area, volume, speed, etc.
Page 4
Systems of Units:
C.G.S (cm, g, s)
F.P.S (ft, lb, s)
M.K.S (m, kg, s)
SI (standard units with additional quantities).
Page 5
Dimensional Analysis: Expresses dependence on fundamental quantities (M, L, T). Examples:
Speed: [M^0L^1T^{-1}]
Force: [M^1L^1T^{-2}]
Page 6
Dimensional Constants vs. Variables:
Constants: Fixed dimensions (e.g., Planck's constant).
Variables: Dimensions change (e.g., velocity, force).
Page 7
Homogeneity of Dimensions: All terms in a valid equation must maintain the same dimensions. Useful in verifying equations.
Page 8
Examples:
Validating S = ut + \frac{1}{2}at^2 from dimensional integrity.
Analyzing the Vande Waals equation for gas.
Page 9
Vector vs. Scalar:
Scalars: Only magnitude (e.g., mass, speed).
Vectors: Magnitude and direction (e.g., force, velocity).
Page 10
Differentiation of Vectors:
Describes motion through displacement, velocity, and acceleration.
Page 11
Newton’s Laws of Motion:
First Law: Objects remain at rest or uniform motion unless acted upon by net external forces.
Second Law: F = ma (force proportional to acceleration).
Third Law: Action and reaction forces.
Page 12
Gravitation: Study of forces among masses. Introduced by Newton (F = \frac{Gm1m2}{r^2}).
Page 13
Kepler’s Laws: Describe planetary motion.
Law of Ellipses: Planets orbit in ellipses.
Law of Equal Areas: Equal areas covered in equal times.
Harmonic Law: T^2 \propto r^3.
Page 14
Escape Velocity: Minimum speed to escape gravitational pull, v_{escape} = \sqrt{\frac{2GM}{r}}.
Page 15
Orbital Mechanics: Studies motion in orbit influenced by gravity. Key equations include circular orbit velocity: v_{orbit} = \sqrt{\frac{GM}{r}}.
Page 16
Applications: Satellite communication, weather monitoring, GPS.
Page 17
Gravitational waves: Ripples in spacetime caused by massive objects.
Page 18
Conservation Laws: Energy and momentum conservation principles.
Page 19
Kinematics Summary: Types of motion characterized by velocity and acceleration.
Page 20
Torque and Rotational Dynamics: Analyzing forces causing rotations, \tau = r \times F .
Page 21
Circular Motion: Relation of particle movement in circular paths to angular and linear quantities.
Page 22
Moment of Inertia: Mass distribution relative to axis of rotation.
Page 23
Conservation of Angular Momentum: The total angular momentum remains constant in absence of external torque.
Page 20 - Torque and Rotational Dynamics:
Evaluates forces causing rotations and their effects on motion. Force does not affect an object in rotation just by its presence—its point of application matters too.
Key Formula:
Torque:
τ = r × F
Where:
τ = torque (measured in Newton-meters)
r = perpendicular distance from the axis of rotation to the line of action of the force
F = magnitude of the applied force
Torque and its Importance:
Torque gives an object its rotational force. In analyzing problems:
Direction: The direction of torque is determined by the right-hand rule, affecting how the object will rotate.
Equilibrium Conditions: When solving problems, ensure the sum of torques equals zero for rotational equilibrium conditions.
Example: If a wrench applies a force to a nut, the distance from the nut to where the force is applied affects how effective that force will be.
Page 21 - Circular Motion:
Examines the motion of objects traveling along circular paths. The forces acting on circular motion are directed towards the center, known as centripetal forces. Understanding this helps predict object behavior in circular paths.
Key Formulas:
Centripetal Acceleration:
a_c = v²/r
Where:
a_c = centripetal acceleration (m/s²)
v = tangential velocity (m/s)
r = radius of the circular path (m)
Centripetal Force:
Fc = m ac = m(v²/r)
Where:
F_c = centripetal force (N)
m = mass of the object (kg)
Problem Solving Strategies:
Identify the mass and speed of the object to determine centripetal force.
Use the relationship of tangential velocity and radius to solve for the unknowns in motion problems.
Example: When a car takes a turn, the required force to keep it in the circular path is provided by friction between the tires and the road.
Page 22 - Moment of Inertia:
A measure of an object’s resistance to changes in its rotational motion. It depends on both the object's mass and how that mass is distributed relative to the axis of rotation.
Key Formula:
Moment of Inertia:
I = Σ m r²
Where:
I = moment of inertia (kg·m²)
m = mass of each point (kg)
r = distance from the axis of rotation (m)
Common Examples:
For a solid disk rotating about its center:
I = (1/2) m R²
For a thin ring rotating about its center:
I = m R²
Problem Solving Insights:
To calculate the moment of inertia, determine the shape of the object and apply the respective formula.
For complex objects, break them down into simpler shapes, calculate each moment of inertia, and sum them up.
Example: To find the moment of inertia for a composite object like L-shaped structures, treat each leg of the L as a separate shape, calculate each leg's inertia, and add them together.
Page 23 - Angular Velocity and Acceleration:
Angular velocity describes how quickly an object rotates, while angular acceleration measures the rate of change of angular velocity.
Key Formulas:
Angular Velocity:
ω = Δθ/Δt
Where:
ω = angular velocity (rad/s)
Δθ = change in angle (radians)
Δt = change in time (seconds)
Angular Acceleration:
α = Δω/Δt
Where:
α = angular acceleration (rad/s²)
Practical Application:
Relate linear quantities to rotational motion through the formula:
v = rω
Where:
v = linear velocity (m/s)
r = radius of the circular path (m)
ω = angular velocity (rad/s)
Study scenarios that require the understanding of when an object is starting to spin or stop.
Example: When a record player rotates a vinyl record, the angular velocity will help determine its speed, while angular acceleration will show how quickly it speeds up or slows down.
Summary
Overall Problem Solving Strategies:
Carefully read the problem
Page 1 - PHYSICS:
Study of nature and properties of matter and energy including heat, light, sound, electricity, and magnetism.
Page 2 - Course Outline Topics:
Space and time
Units and dimensions
Vectors and scalars
Kinematics
Newton’s Laws of motion
Conservation principles
Rotational motion
Gravitation
Page 3 - Measurement:
Process of comparing an unknown physical quantity with a known fixed physical quantity (e.g., unit). Units should be well-defined and reproducible.
Standard Units:
Fundamental units: Length, mass, time, and others.
Derived units: Area, volume, speed, etc.
Page 4 - Systems of Units:
C.G.S (cm, g, s)
F.P.S (ft, lb, s)
M.K.S (m, kg, s)
SI (standard units with additional quantities).
Page 5 - Dimensional Analysis:
Expresses dependence on fundamental quantities (M, L, T). Examples:
Speed: [M^0L^1T^{-1}]
Force: [M^1L^1T^{-2}]
Page 6 - Dimensional Constants vs. Variables:
Constants: Fixed dimensions (e.g., Planck's constant).
Variables: Dimensions change (e.g., velocity, force).
Page 7 - Homogeneity of Dimensions:
All terms in a valid equation must maintain the same dimensions. Useful in verifying equations.
Page 8 - Examples:
Validating S = ut + \frac{1}{2}at^2 from dimensional integrity.
Analyzing the Vande Waals equation for gas.
Page 9 - Vector vs. Scalar:
Scalars: Only magnitude (e.g., mass, speed).
Vectors: Magnitude and direction (e.g., force, velocity).
Page 10 - Differentiation of Vectors:
Describes motion through displacement, velocity, and acceleration.
Key Formulas:
Displacement: \Delta r = rf - ri
Velocity: v = \frac{\Delta r}{\Delta t}
Acceleration: a = \frac{\Delta v}{\Delta t}
Page 11 - Newton’s Laws of Motion:
First Law: Objects remain at rest or uniform motion unless acted upon by net external forces.
Second Law: F = ma (force proportional to acceleration).
Third Law: Action and reaction forces.
Page 12 - Gravitation:
Study of forces among masses. Introduced by Newton: F = \frac{G m1 m2}{r^2} where:
G = gravitational constant
m1, m2 = masses involved
r = distance between the centers of the two masses
Page 13 - Kepler’s Laws:
Describe planetary motion.
Law of Ellipses: Planets orbit in ellipses.
Law of Equal Areas: Equal areas covered in equal times.
Harmonic Law: T^2 \propto r^3 where T is the orbital period and r is the average distance from the sun.
Page 14 - Escape Velocity:
Minimum speed to escape gravitational pull: v_{escape} = \sqrt{\frac{2GM}{r}} where:
M = mass of the celestial body
r = radius from the center of the body to the point of escape
Page 15 - Orbital Mechanics:
Studies motion in orbit influenced by gravity. Key equations include circular orbit velocity: v_{orbit} = \sqrt{\frac{GM}{r}}
Page 16 - Applications:
Satellite communication, weather monitoring, GPS.
Understanding orbital mechanics is critical for the placement and functioning of satellites.
Page 17 - Gravitational Waves:
Ripples in spacetime caused by massive objects.
Detected by observatories like LIGO, which measure tiny changes in distance between mirrors caused by passing waves.
Page 18 - Conservation Laws:
Energy and momentum conservation principles.
Key Formulas:
Conservation of Mechanical Energy: E_{total} = KE + PE
Linear Momentum: p = mv
Page 19 - Kinematics Summary:
Types of motion characterized by velocity and acceleration.
Key Concepts:
Uniform Motion: Constant velocity, thus acceleration = 0.
Non-uniform Motion: Changing velocity, thus acceleration is non-zero.
Page 20 - Torque and Rotational Dynamics:
Analyzing forces causing rotations, \tau = r \times F.
Key Formula:
Torque:
\tau = r \times F
Where:
\tau = torque (measured in Newton-meters)
r = perpendicular distance from the axis of rotation to the line of action of the force
F = magnitude of the applied force
Torque and its Importance: Torque gives an object its rotational force. In analyzing problems:
Direction: The direction of torque is determined by the right-hand rule, affecting how the object will rotate.
Equilibrium Conditions: When solving problems, ensure the sum of torques equals zero for rotational equilibrium.
Example: If a wrench applies a force to a nut, the distance from the nut to where the force is applied affects efficiency.
Page 21 - Circular Motion:
Examines the motion of objects traveling along circular paths. The forces acting on circular motion are directed towards the center, known as centripetal forces. Understanding this helps predict object behavior in circular paths.
Key Formulas:
Centripetal Acceleration:
a_c = \frac{v^2}{r}
Where:
a_c = centripetal acceleration (m/s²)
v = tangential velocity (m/s)
r = radius of the circular path (m)
Centripetal Force:
Fc = mac = m \left(\frac{v^2}{r}\right)
Where:
F_c = centripetal force (N)
m = mass of the object (kg)
Problem Solving Strategies:
Identify the mass and speed of the object to determine centripetal force.
Use the relationship of tangential velocity and radius to solve for unknowns.
Example: When a car takes a turn, require force to keep in the circular path is provided by friction.
Page 22 - Moment of Inertia:
A measure of an object’s resistance to changes in its rotational motion. It depends on both the object's mass and how that mass is distributed relative to the axis of rotation.
Key Formula:
Moment of Inertia:
I = \Sigma m r^2
Where:
I = moment of inertia (kg·m²)
m = mass of each point (kg)
r = distance from the axis of rotation (m)
Common Examples:
For a solid disk rotating about its center:
I = \left(\frac{1}{2}\right) m R^2
For a thin ring rotating about its center:
I = m R^2
Problem Solving Insights:
Calculate moment of inertia by determining shape and applying formula.
For complex objects, break into simpler shapes and sum inertias.
Example: Finding moment of inertia for L-shaped structures by treating each leg as separate.
Page 23 - Angular Velocity and Acceleration:
Angular velocity describes how quickly an object rotates, while angular acceleration measures the rate of change of angular velocity.
Key Formulas:
Angular Velocity:
\omega = \frac{\Delta\theta}{\Delta t}
Where:
\omega = angular velocity (rad/s)
\Delta\theta = change in angle (radians)
\Delta t = change in time (seconds)
Angular Acceleration:
\alpha = \frac{\Delta\omega}{\Delta t}
Where:
\alpha = angular acceleration (rad/s²)
Practical Application:
Relate linear quantities to rotational motion:
v = r \omega
Where:
v = linear velocity (m/s)
r = radius (m)
\omega = angular velocity (rad/s)
Study scenarios of starting or stopping motion.
Example: Record player speed using angular velocity