6.5 Rolling Motion of Orbiting Satellites

• 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 \(5 \, \text{rad/s}\)?

  $\omega_{2} \approx 3.33 \, \text{rad / s}$
• 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 =$$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 =$$\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