General Physics 1 - Torque and Angular Momentum

General Physics 1 - Second Quarter

• Week 1: Torque and Angular Momentum

  • Torque is derived from the Latin word torquere, meaning "to twist."
  • Torque is the turning force, and it's a vector quantity.
  • The unit of measurement for torque is Newton-meter (Nm).
  • Torque can be viewed as having two parts: one in the direction of the rotation axis, and the other perpendicular to the axis.
  • Torque (τ) = Force (F) × Moment arm (l) = rFsinθ, where r is the perpendicular distance, F is the force, and θ is the angle between r and F.
  • Torque is positive when the force tends to produce counterclockwise rotation and negative for clockwise rotation.
  • Torque does not change the speed of rotation, but it changes the direction of spin (precession).

• Engagement (Page 2)

  • Force is most effective in producing torque when exerted perpendicular to the wrench.
  • Torque is calculated as force multiplied by the lever arm.
  • Example problem: calculating the force needed to achieve a specific torque when tightening a spark plug. Example torque problem: calculating the force needed to apply torque to open a door.
  • More examples of calculating torque in different scenarios.

• Assimilation (Page 3)

  • Equilibrium requires net external force and net external torque to be zero, for rotational equilibrium.
  • Torque is the rotational equivalent of force and is a measure of how effective a force is in changing or accelerating rotation.
  • The second condition for equilibrium is that the net external torque on a system must be zero.
  • Torques in opposite directions are assigned opposite signs (counterclockwise positive, clockwise negative).

• Week 2: Rotational Kinematics & Moment of Inertia

  • Torque causes rotation.
  • Angular acceleration relates to the rate of change of angular velocity and is the rotational analog of linear acceleration.
  • Angular velocity (ω) = Δθ/Δt, where Δθ is the change in angle and Δt is the change in time.
  • Linear velocity (v) = rω, where r is the radius of curvature.
  • Angular acceleration (α) = Δω/Δt.
  • The moment of inertia (I) is a measure of an object's resistance to changes in its rotation.
  • Moment of inertia is the rotational equivalent of mass.
  • It depends on mass and axis of rotation.

• Calculating Angular Acceleration and Deceleration of Bike Wheel (Page 5)

  • The problem provides data on initial and final angular velocity and time.
  • The equation for angular acceleration formula (α = Δω/Δt) is used to calculate the angular velocity. (Δω: change in angular velocity, Δt: change in time)
  • Units are converted to standard units for angular acceleration (rad/s²).

• Moment of Inertia (Page 6)

  • Object's resistance to changes in rotation; calculated as sum of masses at different distances from axis of rotation.
  • The total moment of inertia depends on mass and the axis of rotation selected.
  • A rotating mass possesses kinetic energy, dependent on moment of inertia and angular velocity.

• Assessment (Page 7)

  • Imagine a merry-go-round. Compare the kinetic energy of two kids sitting at different distances.

• Week 3-4: Newton's Law of Universal Gravitation & Kepler's Laws of Planetary Motion

  • Newton compared the acceleration of the moon to that of objects on Earth.
  • Objects with greater mass attract each other gravitationally with more force.
  • Universal Law of Gravitation explains this.
  • F = Gm1m2/r^2, where G is the universal gravitational constant, m1 and m2 are masses, and r is the distance between their centers.
  • Gravitational force is directly proportional to the masses of the interacting objects but inversely proportional to the square of the distance between their centers.

• Engagement and Assessment (Page 9, 10)

  • Gravitational force between objects is equal and opposite. Objects with greater mass experience greater acceleration when attracting.
  • Heavier objects experience larger gravitational attractive, gravitational interaction between objects.
  • Gravitational force between objects is equal and opposite, regardless if one is a heavier object or not. Heavier objects do experience greater acceleration if experiencing forces of equal magnitude to one another. If both objects experience and have the same forces, however, the objects will move and accelerate at the same rate.
  • Doubling the distance between two objects reduces the gravitational force to 1/4 of its original value.
  • Kepler's three laws of planetary motion were developed to describe the mechanics of planetary motion, describing elliptical motion, equal area in equal time, and ratio of the orbital periods and orbital radii.

• Week 5: Periodic Motion and Waves

  • Periodic motion is motion that repeats at regular intervals.
  • Mechanical waves require a medium to propagate and can be transverse or longitudinal.
  • Defining frequency and periods.

• Week 6: Sound

  • Sound waves cannot travel through a vacuum.
  • Relationship between speed of sound (v_w), frequency (f), and wavelength (λ): v_w= fλ.
  • Standing waves occur when waves reflect from the ends of a string/medium which creates nodes and antinodes.
  • Doppler Effect: Apparent change in frequency of a wave, like sound, due to relative motion between source and observer.
  • Inverse Square Law: Sound intensity decreases with the square of the distance from the source.

• Week 7: Specific Gravity, Pressure, and Buoyancy

  • Matter exists as solid, liquid, or gas, and is often measured by density.
  • Density (ρ) = Mass (m) / Volume (V).
  • Specific gravity is the ratio of the density of a substance to the density of water at a specific temperature (usually 20°C).
  • Pascal's Principle: Pressure applied to an enclosed fluid is transmitted equally in all directions.
  • Bernoulli's Principle: As the speed of a fluid increases, its pressure decreases.
  • Archimedes' Principle: The buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object.

• Week 8-9: Laws of Thermodynamics

  • Thermodynamics deals with heat energy and its relationships to other forms of energy.
  • The First Law of Thermodynamics is the principle of conservation of energy, as applied to thermal systems.
  • Entropy is a measure of the disorder of a system.
  • The Second Law of Thermodynamics describes the direction of energy flow and establishes the concept of entropy. The entropy of an isolated system can increase, but it never decrease.
  • The Third Law of Thermodynamics describes the behavior of systems as their temperature approaches absolute zero. The entropy of a system approaches a constant value as the temperature approaches zero.

• Assessment Questions (Various Weeks)

  • Includes a variety of conceptual and calculation questions on topics covered in the materials.