Summary of "[Vật Lý 11] Bài 3: Phương Trình Vận tốc - Gia Tốc | Chương Trình SGK Mới"

Summary of [Vật Lý 11] Bài 3: Phương Trình Vận tốc - Gia Tốc | Chương Trình SGK Mới

This video lesson covers Lesson 3 from the new Grade 11 Physics curriculum, focusing on the velocity and acceleration equations in harmonic oscillation. The instructor explains the theoretical foundations, key formulas, phase relationships, and demonstrates example problems step-by-step, emphasizing understanding through the phase circle method.

Main Ideas and Concepts

1. Displacement, Velocity, and Acceleration Equations in Harmonic Motion

Displacement equation: [ x = a \cos(\omega t + \varphi) ] where:
- (a) = amplitude
- (\omega) = angular frequency
- (\varphi) = initial phase
Velocity equation: Derived as the time derivative of displacement: [ v = -a \omega \sin(\omega t + \varphi) = a \omega \cos\left(\omega t + \varphi + \frac{\pi}{2}\right) ]
- Maximum velocity: [ v_{\max} = \omega a ]
- Velocity leads displacement by a phase of (\pi/2) (90°).
Acceleration equation: Derived as the time derivative of velocity: [ a = -\omega^2 a \cos(\omega t + \varphi) = \omega^2 a \cos\left(\omega t + \varphi + \pi\right) ]
- Acceleration leads velocity by (\pi/2) and is out of phase with displacement by (\pi) (180°).
- Maximum acceleration: [ a_{\max} = \omega^2 a ]
- Relationship between acceleration and displacement: [ a = -\omega^2 x ]

2. Key Properties of Harmonic Oscillation

The angular frequency (\omega) relates to the period (T) and frequency (f) as: [ \omega = \frac{2\pi}{T}, \quad f = \frac{1}{T} ]
Displacement, velocity, and acceleration share the same angular frequency, period, and frequency.
Velocity and acceleration are harmonic functions of time like displacement.
Velocity is zero at the extreme positions (amplitudes) because the object changes direction there.
Velocity is maximum at the equilibrium position, with the sign indicating direction:
- Positive velocity when moving in the positive direction.
- Negative velocity when moving in the negative direction.
Speed is the absolute value of velocity (always positive), maximum at equilibrium position, zero at extreme positions.

3. Phase Relationships and the Phase Circle

The phase circle is a visual mnemonic tool to understand phase differences among displacement, velocity, and acceleration.
Velocity leads displacement by (\pi/2).
Acceleration leads velocity by (\pi/2).
Acceleration is out of phase with displacement by (\pi).
These phase shifts explain the behavior of velocity and acceleration relative to displacement during oscillation.
Mastery of the phase circle simplifies solving problems without complicated trigonometric equations.

4. Problem-Solving Methodology

To write displacement, velocity, and acceleration equations:

Identify amplitude (a) from the graph (peak displacement).
Calculate angular frequency (\omega = \frac{2\pi}{T}) using the period (T).
Determine initial phase (\varphi) using the position and direction of the object at (t=0), often by referencing the phase circle.
Write the displacement equation: [ x = a \cos(\omega t + \varphi) ]
Write the velocity equation: [ v = \omega a \cos\left(\omega t + \varphi + \frac{\pi}{2}\right) ]
Write the acceleration equation: [ a = \omega^2 a \cos(\omega t + \varphi + \pi) ]

To find maximum speed and acceleration:

Maximum speed occurs at the equilibrium position (x=0).
Maximum acceleration occurs at the extreme positions (x = \pm a).
Use the relationships: [ v_{\max} = \omega a, \quad a_{\max} = \omega^2 a ]

To analyze graphs (displacement, velocity, acceleration vs. time):

Identify key points such as zero crossings, maxima, and minima.
Use these points to infer phase, amplitude, and period.
Apply phase circle reasoning to determine initial phase.

Summary of Example Problems

Example 1: Given amplitude and period, find displacement and velocity equations; determine when the object reaches maximum speed.
Example 2: Using a displacement graph, find amplitude, period, initial phase, and write velocity and acceleration equations; analyze times for maximum speed and zero velocity.
Example 3: Given a velocity-time graph, deduce velocity and displacement equations and interpret phase; find times when velocity is zero or maximum.
Acceleration Examples: Given acceleration-time graphs, find maximum acceleration, period, initial phase; write acceleration and displacement equations; calculate times for zero acceleration and maximum acceleration.

Important Reminders

Distinguish clearly between velocity (vector, signed) and speed (scalar, always positive).
Memorize the formulas for displacement, velocity, and acceleration, including phase shifts.
Master the phase circle method for quick and intuitive problem solving.
Understand that velocity leads displacement by (\pi/2), acceleration leads velocity by (\pi/2), and acceleration is out of phase with displacement by (\pi).
All three quantities share the same angular frequency, period, and frequency.

Speakers / Sources

Main Speaker: The teacher/instructor presenting the lesson and guiding through theory and examples.
No other speakers or external sources are identified.

This summary captures the core theoretical explanations, mathematical formulations, problem-solving techniques, and pedagogical emphasis on phase relationships in harmonic oscillation as presented in the video.