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Rolling Motion (Free Wheels) quiz

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  • What is the main difference between a fixed wheel and a free wheel in rolling motion?
    A fixed wheel rotates around a fixed axis with no movement of its center of mass, while a free wheel both rotates and translates, so its center of mass moves.
  • In the context of rolling motion, what does the velocity of the center of mass (V_CM) represent?
    V_CM represents the translational velocity of the wheel's center of mass as it moves along a surface.
  • What is the key equation relating the velocity of the center of mass and angular velocity for a rolling wheel?
    The key equation is V_CM = R * omega, where R is the radius of the wheel and omega is its angular velocity.
  • When does the equation V_CM = R * omega apply to a rolling wheel?
    This equation applies only when the wheel is rolling without slipping.
  • What is the velocity of the top point of a rolling wheel relative to the ground?
    The velocity at the top of the wheel is 2 * R * omega, which is twice the velocity of the center of mass.
  • What is the velocity of the bottom point of a rolling wheel relative to the floor?
    The velocity at the bottom of the wheel is zero relative to the floor.
  • How do you calculate the angular speed (omega) of a rolling wheel if you know V_CM and R?
    Angular speed omega is calculated as omega = V_CM / R.
  • If a wheel of radius 0.3 m rolls without slipping at 10 m/s, what is its angular speed?
    The angular speed is omega = 10 / 0.3 = 33.3 radians per second.
  • Why is the velocity at the bottom of a rolling wheel zero relative to the floor?
    Because the rotational and translational velocities at that point cancel each other out.
  • What is the condition required for the rolling motion equations to be valid?
    The wheel must roll without slipping for the equations to be valid.
  • In rolling motion, what does 'rolling without slipping' mean?
    It means that the point of contact between the wheel and the surface does not slide; it is momentarily at rest relative to the surface.
  • How does the velocity at the top of a rolling wheel compare to the velocity of its center of mass?
    The velocity at the top is twice the velocity of the center of mass.
  • For a fixed wheel, what is the velocity of the center of mass?
    For a fixed wheel, the velocity of the center of mass is zero.
  • What practical example is used to illustrate the difference between fixed and free wheels?
    A roll of toilet paper is used, with a fixed roll representing a fixed axis and a rolling roll representing a free axis.
  • What is the formula for the velocity at the top, center, and bottom of a rolling wheel?
    The velocities are: top = 2R*omega, center = R*omega, and bottom = 0 (relative to the floor).