6.5 Rolling Motion of Orbiting Satellites

Cards (33)

  • What two types of motion combine to define rolling motion?
    Translation and rotation
  • What is the formula for eccentricity in orbital motion?
    e = \sqrt{1 - \frac{b^{2}}{a^{2}}}</latex>
  • Moment of inertia depends on an object's mass distribution and shape.

    True
  • What shape characterizes the path of a satellite in orbital motion?
    Ellipse
  • The shape of the orbit is an ellipse
  • The time to complete one orbit is called the orbital period
  • In the formula for kinetic energy, \(\omega\) represents the angular velocity
  • In linear motion, mass is analogous to the moment of inertia
  • What is the measure of an object's rotational motion called?
    Angular momentum
  • Match the conservation law with its conserved quantity:
    Conservation of Mechanical Energy ↔️ Total energy (kinetic + potential)
    Conservation of Angular Momentum ↔️ Angular momentum
  • The linear velocity of a rolling object is equal to its angular velocity times its radius.

    True
  • What is the new angular velocity of a satellite if its moment of inertia increases from \(1000 \, \text{kg m}^{2}\) to \(1500 \, \text{kg m}^{2}\) and its initial angular velocity is \(5 \, \text{rad/s}\)?
    ω2≈3.33 rad / s\omega_{2} \approx 3.33 \, \text{rad / s}
  • When an object rolls without slipping, its linear velocity is related to its angular velocity.

    True
  • Orbital motion focuses primarily on gravitational forces rather than frictional forces.
  • Orbital motion primarily concerns gravitational forces rather than frictional forces.
    True
  • The eccentricity of a perfect circle is 0.

    True
  • The gravitational constant is represented by the letter G.
    True
  • What does the moment of inertia represent?
    Resistance to rotational motion
  • What is the sum of kinetic and potential energy called?
    Mechanical energy
  • Angular momentum remains constant when no external torque acts
  • What is the relationship between linear velocity and angular velocity when an object rolls without slipping?
    v=v =Rω R\omega
  • Which two conservation laws are used to analyze the motion of rolling satellites?
    Mechanical energy and angular momentum
  • Orbital motion describes the movement of a satellite around a central body
  • What is the formula for rotational kinetic energy?
    KE = \frac{1}{2} I \omega^{2}</latex>
  • Moment of inertia is the rotational equivalent of mass
  • What is the path followed by a satellite called?
    Orbit
  • What is the formula for the orbital velocity of a satellite?
    v=v =GM(2/r−1/a) \sqrt{GM(2 / r - 1 / a)}
  • What type of energy does an object have due to its spinning motion?
    Kinetic energy
  • The moment of inertia depends on the object's mass distribution and shape.
    True
  • Mechanical energy remains constant in the absence of external forces.
    True
  • Conservation of angular momentum determines the satellite's orbit shape and orientation.

    True
  • The unit for linear velocity is meters per second
  • The potential energy of a satellite is given by PE = - \frac{GMm}{r}</latex>, where \(G\) is the gravitational constant