AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 6: Energy & Momentum of Rotating SystemsExamples of Rotational Systems

Examples of Rotational Systems (College Board AP® Physics 1: Algebra-Based): Flashcards

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  • FrontRolling

    State the equation for the total kinetic energy of a rolling object.

Cards in this collection (23)

  • State the equation for the total kinetic energy of a rolling object.

    K_{\text{total}} = K_{\text{trans}} + K_{\text{rot}} = \frac{1}{2} m v^{2} + \frac{1}{2} I \omega^{2}

    • m = mass of the object (kg)

    • v = linear velocity (m/s)

    • I = rotational inertia (kg·m2)

    • \omega = angular velocity (rad/s)

  • What is true of the point of contact when an object rolls without slipping?

    The point of contact between the object and the surface is at rest (no relative motion).

  • State the equation relating linear and angular velocity for an object rolling without slipping.

    v_{\text{cm}} = r \omega

    • v_{\text{cm}} = velocity of the center of mass (m/s)

    • r = radius of the object (m)

    • \omega = angular speed (rad/s)

  • Why is no energy dissipated when an object rolls without slipping?

    Only static friction acts, and static friction does no work.

  • What energy transfer occurs when a ball rolls without slipping down a ramp from rest?

    Gravitational potential energy is transferred to both translational and rotational kinetic energy.

  • Why is energy dissipated when an object rolls while slipping?

    Kinetic friction acts because there is relative motion at the point of contact, and it does work.

  • True or False?

    When an object rolls while slipping, v_{\text{cm}} = r \omega still holds.

    False.

    The center-of-mass motion cannot be directly related to the rotational motion, so v_{\text{cm}} \neq r \omega.

  • When an object rolls without slipping, the distance traveled by its center of mass equals the .......... that has been in contact with the ground.

    When an object rolls without slipping, the distance traveled by its center of mass equals the arc length that has been in contact with the ground.

  • Define the gravitational potential energy of a system.

    The gravitational potential energy of a system is the work done to assemble the system from infinite separation of its components.

  • State the equation for the gravitational potential energy of a satellite–central-object system.

    U_{g} = - G \frac{m_{1} m_{2}}{r}

    • U_{g} = gravitational potential energy of the system (J)

    • G = universal gravitational constant (N·m2/kg2)

    • m_{1} = mass of the central body (kg)

    • m_{2} = mass of the satellite (kg)

    • r = distance between the centers of the masses (m)

  • State the equation for the orbital speed of a satellite in a circular orbit.

    v = \sqrt{\frac{G M}{r}}

    • v = orbital speed of the satellite (m/s)

    • G = universal gravitational constant (N·m2/kg2)

    • M = mass of the central body (kg)

    • r = distance between the centers of the masses (m)

  • State the equation for the total mechanical energy of a satellite in a circular orbit.

    E_{\text{total}} = - \frac{G M m}{2 r}

    • E_{\text{total}} = total mechanical energy of the system (J)

    • G = universal gravitational constant (N·m2/kg2)

    • M = mass of the central body (kg)

    • m = mass of the satellite (kg)

    • r = distance between the centers of the masses (m)

  • Where in an elliptical orbit is a satellite's speed greatest, and why?

    At the point closest to the central object. Angular momentum is conserved, so the shortest radius gives the highest speed.

  • Why is the angular momentum of a satellite in an elliptical orbit constant?

    Gravity acts along the radius toward the central object, so it produces no torque and there is no net external torque on the system.

  • In a circular orbit of a given radius, all satellites travel at the same speed regardless of their ...........

    In a circular orbit of a given radius, all satellites travel at the same speed regardless of their mass.

  • True or False?

    The total mechanical energy of a satellite in an elliptical orbit changes as its distance from the central object changes.

    False.

    The total mechanical energy is constant. Only the satellite's kinetic energy and the system's gravitational potential energy change, and they change in opposite ways.

  • Define escape velocity.

    Escape velocity is the minimum velocity that will allow an object to escape a gravitational field with no further energy input.

  • State the equation for escape velocity.

    v_{\text{esc}} = \sqrt{\frac{2 G M}{r}}

    • v_{\text{esc}} = escape velocity (m/s)

    • G = universal gravitational constant (N·m2/kg2)

    • M = mass of the central object (kg)

    • r = distance between the satellite and the center of the central object (m)

  • What is the mechanical energy of the satellite–central-object system at escape velocity?

    Zero.

  • What is the speed of a satellite launched at escape velocity when it is an infinite distance from the central body?

    Zero.

  • Why is the escape velocity from Earth the same for a satellite and a tennis ball?

    The mass of the escaping object cancels when the kinetic and gravitational potential energies are equated, so v_{\text{esc}} depends only on the central body's mass and the distance r.

  • Escape velocity assumes that the only force exerted on the satellite is the .......... of the central object.

    Escape velocity assumes that the only force exerted on the satellite is the gravitational attraction of the central object.

  • True or False?

    A rocket must reach Earth's escape velocity to enter an orbit around Earth.

    False.

    An orbit is still within Earth's gravitational field, so less work is needed than to escape the field entirely.

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