Rotational Motion and Dynamics Quiz

Rotational Motion (Momentum)

• Rotational motion, also called angular motion, describes the motion of objects in a circular path.
• Uniform circular motion refers to objects moving at a constant speed in a circle.
• Angular displacement (θ) is the angle swept out by the radius to the object, measured in radians (rad).
• Angular velocity (ω) is the rate of change of angular displacement, measured in radians per second (rad/s).
• Angular acceleration (α) is the rate of change of angular velocity, measured in radians per second squared (rad/s²).
• Counterclockwise motion is typically considered positive, while clockwise is negative.

Rotational Dynamics

• Torque (τ) is a measure of the force's ability to cause rotation.
• Torque is calculated as the product of force (F) and the lever arm (r): τ = F * r
• Torque is a vector quantity, and its direction is determined by the cross product of force and lever arm.
• Torque is positive for counterclockwise rotation and negative for clockwise rotation.
• Static equilibrium occurs when an object is at rest, not rotating or translating.

Angular Momentum

• Angular momentum is a quantity that describes how difficult it is to change the rotational motion of a spinning body.
• It is relevant for single particles with known momentum.

Gravity

• Gravitational force is the force of attraction between two objects.
• Newton's Law of Gravitation describes the force of attraction between two bodies.
• The constant in Newton's Law of Gravitation (G) is approximately 6.674 x 10⁻¹¹ N m²/kg².

Orbits

• The only force acting on a satellite in a circular orbit is the gravitational attraction of the Earth.
• Satellites are constantly falling around the Earth.
• Kepler's Laws of Planetary Motion describe the motion of planets around the sun.
• The first law states that planets move in elliptical orbits with the sun at one focus.
• The second law describes that a line connecting a planet to the sun sweeps out equal areas in equal intervals of time.
• The third law relates the orbital period of a planet to its distance from the sun.

Mechanical Waves

• An oscillation or vibration is a "wiggle" over time.
• Damped harmonic oscillations have amplitude that decreases over time.
• Under damped oscillation – amplitude decreases until it becomes 0.
• Critically and overdamped oscillation – return to equilibrium without oscillation
• Mechanical waves require a medium to propagate (travel through).
• Types of Mechanical Waves:
  • Transverse waves: Particle motion is perpendicular to wave direction.
  • Longitudinal waves: Particle motion is parallel to wave direction.

Sound Waves

• Sound waves are longitudinal waves.
• Sound frequency is the detectable range.
  • Audible range, ultrasonic frequencies, and infrasonic frequencies.
• Pitch is how high or low a sound is perceived; it relates to frequency.
• Loudness is related to the pressure amplitude.
• Timbre or tone color is how different sounds are perceived – which object made the sound.
• Doppler effect is the change in the frequency of sound as a source and observer move relative to each other.

Fluid Mechanics

• Fluids include liquids and gases.
• Density (ρ) is the mass per unit volume (kg/m³).
• Pressure is the force per unit area (Pa).
• Pascal's Principle – pressure applied to a confined fluid is transmitted equally throughout the fluid.
• Archimedes' Principle – buoyant force on a submerged object is equal to the weight of the fluid displaced.
• Bernoulli's Principle – faster-moving fluid exerts less pressure.

Temperature

• Temperature is a measure of the hotness or coldness of an object.
• Common temperature scales include Celsius (°C), Fahrenheit (°F), and Kelvin (K).
• Thermal expansion is the change in an object's size due to a temperature change.
• Heat transfer mechanisms are conduction, convection, and radiation.
• An isolated system does not exchange energy or mass with its surroundings.

Laws of Thermodynamics

• The first law of thermodynamics is the law of conservation of energy.
• Heat can be converted into work and work into heat.
• The second law of thermodynamics limits the amount of work that can be obtained from heat.
  • Kelvin-Planck statement, Clausius statement, and entropy statement.
• Heat engines convert heat into work.
• Internal combustion engines and external combustion engines.