28 Questions
What is the expression for the angular velocity of an object in rotational motion?
$\omega = \frac{∆θ}{dt}$
What is the force that causes an object to move in a circular path?
Centripetal force
What is the expression for the angular acceleration of an object in rotational motion?
$α = \frac{∆ω}{dt}$
What is the unit of moment of inertia?
kg m^2
What is the expression for the orbital velocity of a satellite?
$v_o = \sqrt{\frac{GM}{R}}$
What is the expression for the centripetal force acting on an object moving in a circular path?
$F_c = \frac{m v^2}{r}$
What is the effect of the Earth's rotation on the apparent weight of an object?
It decreases the apparent weight
What is the unit of angular displacement?
Radian
What is the expression for the angular momentum of an object?
$L = m v r$
What is the effect of the Earth's shape on the value of g?
It increases the value of g at the poles
What is the formula for the radius of gyration of a semicircular ring?
k = 2r/π
What is the direction of the centripetal force acting on an object moving in a circular path?
Radial towards the center of the circle
What is the formula for the angular momentum of an object rotating about an axis?
L = Iω
What is the relationship between the torque and angular momentum of an object?
τ = dL/dt
What is the formula for the center of curvature of a semicircular disc?
yc = 3π/4r
What is the formula for the torque of an object rotating about an axis?
τ = r × F
What is the formula for the angular velocity of an object rotating about an axis?
ω = dθ/dt
What is the relationship between the moment of inertia and angular momentum of an object?
I = L/ω
What is the direction of the centripetal force?
Toward the center of the circle
A car is traveling in a circular path at a constant speed. What is the direction of the acceleration?
Toward the center of the circle
What is the minimum speed required for a car to complete a vertical circle?
$\sqrt{5gl}$
A conical pendulum has a length of 2 m and a mass of 0.5 kg. What is the period of the pendulum?
2π √(2/g)
What is the expression for the centripetal force?
$mv^2/r$
A car is traveling in a circular path at a constant speed. What is the direction of the net force?
Toward the center of the circle
What is the banking angle of a circular track, given that the coefficient of friction is 0.5 and the radius of the track is 100 m?
tan^(-1)(0.5)
What is the expression for the centripetal acceleration?
$v^2/r$
A car is traveling in a circular path at a constant speed. What is the direction of the force of friction?
Toward the center of the circle
What is the expression for the force of friction on a circular track?
$μ mg cos(θ)$
Study Notes
Rotational Motion
- Angular velocity: ωav = ∆θ / ∆t, ω = dθ / dt
- Angular acceleration: αav = ∆ω / ∆t, α = dω / dt
- Rotation about an axis with constant α: ω = ω0 + αt, θ = ωt + (1/2) αt2
- Moment of Inertia: I = Σmi ri^2, I = mr^2 for a ring or disc
- Angular momentum: L = Iω, L = r × p
- Torque: τ = r × F, τ = dL / dt
- Newton's second law for rotation: τ = Iα
Orbital Motion
- Orbital velocity of a satellite: vo = √(GM/R)
- Escape velocity: ve = √(2GM/R)
Properties of Matter
- Modulus of rigidity: Y = ∆l / l, B = -V ∆V, η = Aθ
- Radius of gyration: k = √(I/m)
Kepler's Laws
- First law: elliptical orbit with sun at one of the foci
- Semimajor axis: a = (a1 + a2) / 2
Units and Constants
- Atomic mass unit: u = 931.49 MeV/c^2
- Stefan-Boltzmann constant: σ = 5.67 × 10^-8 W/(m^2 K^4)
- Rydberg constant: R∞ = 1.097 × 10^7 m^-1
- Bohr magneton: µB = 9.27 × 10^-24 J/T
- Bohr radius: a0 = 0.529 × 10^-10 m
- Standard atmosphere: atm = 1.01325 × 10^5 Pa
- Wien displacement constant: b = 2.9 × 10^-3 m K
Vectors
- Notation: ~a = ax ı̂ + ay ̂ + az k̂
- Magnitude: a = |~a| = √(a_x^2 + a_y^2 + a_z^2)
- Dot product: ~a · ~b = ax bx + ay by + az bz = ab cos θ
- Cross product: ~a × ~b = (ay bz - az by)ı̂ + (az bx - ax bz)̂ + (ax by - ay bx)k̂
Work, Power, and Energy
- Work: W = F~ · S = F S cos θ
- Kinetic energy: K = (1/2) mv^2 = p^2 / 2m
- Potential energy: F = -∂U/∂x for conservative forces
This quiz covers the effects of the non-spherical earth shape and earth rotation on gravity and apparent weight, including rigid body dynamics.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
