Physics Chapter 10: Gravity and Rotation
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Questions and Answers

What is the expression for the angular velocity of an object in rotational motion?

  • $\omega_{av} = \frac{∆θ}{∆t}$
  • $\omega = \sqrt{\frac{mg}{r}}$
  • $\omega = \frac{v}{r}$
  • $\omega = \frac{∆θ}{dt}$ (correct)

    • What is the force that causes an object to move in a circular path?

  • Gravitational force
  • Electromagnetic force
  • Centripetal force (correct)
  • Frictional force

    • What is the expression for the angular acceleration of an object in rotational motion?

  • $α = \frac{∆ω}{dt}$ (correct)
  • $α = \frac{v^2}{r}$
  • $α_{av} = \frac{∆ω}{∆t}$
  • $α = \frac{mg}{r}$

    • What is the unit of moment of inertia?

    <p>kg m^2</p> Signup and view all the answers

    What is the expression for the orbital velocity of a satellite?

    <p>$v_o = \sqrt{\frac{GM}{R}}$</p> Signup and view all the answers

    What is the expression for the centripetal force acting on an object moving in a circular path?

    <p>$F_c = \frac{m v^2}{r}$</p> Signup and view all the answers

    What is the effect of the Earth's rotation on the apparent weight of an object?

    <p>It decreases the apparent weight</p> Signup and view all the answers

    What is the unit of angular displacement?

    <p>Radian</p> Signup and view all the answers

    What is the expression for the angular momentum of an object?

    <p>$L = m v r$</p> Signup and view all the answers

    What is the effect of the Earth's shape on the value of g?

    <p>It increases the value of g at the poles</p> Signup and view all the answers

    What is the formula for the radius of gyration of a semicircular ring?

    <p>k = 2r/π</p> Signup and view all the answers

    What is the direction of the centripetal force acting on an object moving in a circular path?

    <p>Radial towards the center of the circle</p> Signup and view all the answers

    What is the formula for the angular momentum of an object rotating about an axis?

    <p>L = Iω</p> Signup and view all the answers

    What is the relationship between the torque and angular momentum of an object?

    <p>τ = dL/dt</p> Signup and view all the answers

    What is the formula for the center of curvature of a semicircular disc?

    <p>yc = 3π/4r</p> Signup and view all the answers

    What is the formula for the torque of an object rotating about an axis?

    <p>τ = r × F</p> Signup and view all the answers

    What is the formula for the angular velocity of an object rotating about an axis?

    <p>ω = dθ/dt</p> Signup and view all the answers

    What is the relationship between the moment of inertia and angular momentum of an object?

    <p>I = L/ω</p> Signup and view all the answers

    What is the direction of the centripetal force?

    <p>Toward the center of the circle</p> Signup and view all the answers

    A car is traveling in a circular path at a constant speed. What is the direction of the acceleration?

    <p>Toward the center of the circle</p> Signup and view all the answers

    What is the minimum speed required for a car to complete a vertical circle?

    <p>$\sqrt{5gl}$</p> Signup and view all the answers

    A conical pendulum has a length of 2 m and a mass of 0.5 kg. What is the period of the pendulum?

    <p>2π √(2/g)</p> Signup and view all the answers

    What is the expression for the centripetal force?

    <p>$mv^2/r$</p> Signup and view all the answers

    A car is traveling in a circular path at a constant speed. What is the direction of the net force?

    <p>Toward the center of the circle</p> Signup and view all the answers

    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?

    <p>tan^(-1)(0.5)</p> Signup and view all the answers

    What is the expression for the centripetal acceleration?

    <p>$v^2/r$</p> Signup and view all the answers

    A car is traveling in a circular path at a constant speed. What is the direction of the force of friction?

    <p>Toward the center of the circle</p> Signup and view all the answers

    What is the expression for the force of friction on a circular track?

    <p>$μ mg cos(θ)$</p> Signup and view all the answers

    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

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    Description

    This quiz covers the effects of the non-spherical earth shape and earth rotation on gravity and apparent weight, including rigid body dynamics.

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