All Flashcards
What are the differences between distance and displacement?
Distance: Total path length, scalar quantity. Displacement: Change in position, vector quantity.
What are the differences between speed and velocity?
Speed: Rate of motion (magnitude of velocity), scalar quantity. Velocity: Rate of change of position (speed with direction), vector quantity.
Compare horizontal and vertical motion in projectile motion.
Horizontal (x) motion: Constant velocity (no acceleration). Vertical (y) motion: Constant acceleration due to gravity (g).
Compare scalar and vector quantities.
Scalar: Magnitude only (e.g., distance, speed). Vector: Magnitude and direction (e.g., displacement, velocity, acceleration).
How do you calculate the maximum force in a mass-spring system undergoing simple harmonic motion?
The maximum force (Fmax) in a mass-spring system is given by Fmax = mω²x0, where m is the mass, ω is the angular frequency, and x0 is the amplitude of oscillation.
Define the amplitude in the context of simple harmonic motion.
Amplitude in simple harmonic motion is the maximum extent of displacement from the midpoint or equilibrium position.
When is the kinetic energy at its maximum in simple harmonic motion?
The kinetic energy is at its maximum when the mass is at the equilibrium position, moving at its fastest speed. There are two kinetic-energy maxima per oscillation.
Explain how simple harmonic motion is related to uniform circular motion.
Simple harmonic motion can be visualized as the projection of uniform circular motion onto one axis. If an object rotates uniformly in a horizontal circle and this motion is viewed from the side, the up-and-down motion maps out simple harmonic motion.
How are the coordinates x and y linked to the circle's radius r and angle θ with the x-axis in simple harmonic motion?
The horizontal coordinate x and the vertical coordinate y can be derived from the circle's radius r and angle θ by using trigonometric functions: x = r cos(θ) and y = r sin(θ).
What are the equations for the x-projection of point P moving in a circle (in terms of r, ω, and t)?
x = r cos(ωt) and y = r sin(ωt) represent the x and y projections, respectively, where r is the radius, ω is the angular frequency, and t is time.
State the equations for displacement in simple harmonic motion starting from extremes and from the center.
For SHM starting at extremes, x = x0 cos(ωt). For motion starting at the center, x = x0 sin(ωt), where x0 is maximum displacement, ω is angular frequency, and t is time.
How is angular frequency (ω) calculated from the period of oscillation?
ω = 2π / T, where T is the period.
How is the maximum velocity of an object in simple harmonic motion related to angular frequency and amplitude?
The maximum velocity (vmax) in simple harmonic motion is calculated using the formula vmax = ω * A, where ω is the angular frequency, and A is the amplitude.
How do you calculate the maximum acceleration of an object in simple harmonic motion using angular frequency and amplitude?
The maximum acceleration (amax) in simple harmonic motion is given by the formula: amax = ω^2 * A, where ω is the angular frequency and A is the amplitude.
What is the effect of constant velocity?
Zero acceleration.
What is the effect of constant acceleration?
Velocity changes uniformly with time.