chapter 9 simple circular motion and harmonic motion Flashcards
What is the definition of angular displacement?
Angular displacement is the angle through which an object has rotated or moved around a circular path, measured in radians.
What is angular velocity?
Angular velocity is the rate at which an object changes its angular displacement, typically measured in radians per second:
ω = Δθ / Δt
What is the equation for centripetal acceleration?
a_c = v² / r
Where v is the tangential velocity and r is the radius of the circular path.
What is the equation for centripetal force?
F_c = m v² / r
Where m is the mass of the object, v is the velocity, and r is the radius.
What is the relationship between angular velocity and tangential velocity?
Tangential velocity is related to angular velocity by:
v = ωr
What is the period of an object in circular motion?
The time taken for one complete revolution.
T = 2π / ω
What is the frequency of an object in circular motion?
The number of revolutions per second.
f = 1 / T = ω / 2π
What is simple harmonic motion?
SHM is oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position.
F = -kx (Hooke’s Law)
What is the equation for acceleration in SHM?
a = -ω²x
Where a is acceleration, ω is angular frequency, and x is displacement.
What is the equation for velocity in SHM?
v = ±ω√(A² - x²)
Where v is the velocity, ω is angular frequency, A is the amplitude, and x is the displacement.
What is the equation for displacement in SHM?
x = A cos(ωt + φ)
Where A is the amplitude, ω is angular frequency, t is time, and φ is the phase constant.
What is the period of a simple harmonic oscillator?
The time taken for one complete oscillation:
T = 2π / ω
What is the frequency of a simple harmonic oscillator?
The number of oscillations per second:
f = 1 / T = ω / 2π
What is the energy in simple harmonic motion?
The total mechanical energy (E) is constant and is the sum of kinetic and potential energy:
E = 1/2 m ω² A²
Where m is mass, ω is angular frequency, and A is the amplitude.
How is the force in SHM related to displacement?
The restoring force is proportional to displacement and acts in the opposite direction:
F = -kx
