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 (D)</p> Signup and view all the answers

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

<p>$v_o = \sqrt{\frac{GM}{R}}$ (D)</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>$F_c = \frac{m v^2}{r}$ (C)</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 (D)</p> Signup and view all the answers

What is the unit of angular displacement?

<p>Radian (C)</p> Signup and view all the answers

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

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

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

<p>k = 2r/Ï€ (C)</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 (A)</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 (D)</p> Signup and view all the answers

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

<p>Ï„ = dL/dt (C)</p> Signup and view all the answers

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

<p>yc = 3Ï€/4r (B)</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 (D)</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 (A)</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 (D)</p> Signup and view all the answers

What is the direction of the centripetal force?

<p>Toward the center of the circle (C)</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 (B)</p> Signup and view all the answers

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

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

What is the expression for the centripetal force?

<p>$mv^2/r$ (B)</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 (B)</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) (C)</p> Signup and view all the answers

What is the expression for the centripetal acceleration?

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

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

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

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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: Ï„ = r × F, Ï„ = dL / dt
  • Newton's second law for rotation: Ï„ = 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 kÌ‚
  • 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)kÌ‚

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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