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Physics with Calculus: Momentum and Rotational Motion

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Termini in questo insieme (21)

  • What is momentum?

    Momentum is the product of an object's mass and its velocity, representing inertia in motion.

  • Define impulse in physics.

    Impulse is the product of force and the time interval over which it acts, changing an object's momentum.

  • How does impulse relate to change in momentum?

    Impulse equals the change in momentum: \(Impulse = F \times t = \Delta p\).

  • What happens to impulse if the force acts for twice as long?

    The impulse is doubled because impulse is force multiplied by time.

  • Why does a cannonball shot from a long barrel have greater speed?

    Because the force acts over a longer time, producing a greater impulse and thus greater change in momentum.

  • How can extending the time of momentum change reduce force?

    Extending the time over which momentum changes reduces the average force, as seen when hitting a haystack instead of a wall.

  • State the law of conservation of momentum.

    In the absence of external forces, the total momentum of a system remains constant.

  • What is rotational inertia?

    Rotational inertia is an object's resistance to changes in its rotational motion, depending on mass and mass distribution.

  • How does mass distribution affect rotational inertia?

    The farther the mass is from the axis of rotation, the greater the rotational inertia.

  • What is torque?

    Torque is the tendency of a force to cause rotation, depending on force magnitude, direction, and lever arm.

  • How is torque calculated?

    Torque = Force × lever arm (perpendicular distance from axis to force line).

  • Define center of mass and center of gravity.

    Center of mass is the average position of mass; center of gravity is the average position of weight distribution, usually the same point.

  • How is the center of gravity determined experimentally?

    Suspend the object from two points and draw vertical lines; the intersection is the center of gravity.

  • What determines an object's stability related to center of gravity?

    If the vertical line from the center of gravity falls inside the base, the object is stable; outside, it is unstable.

  • What is centripetal force?

    A force directed toward the center of a circular path, keeping an object moving in a circle.

  • Formula for centripetal force?

    \(F_c = \frac{m v^2}{r}\), where m is mass, v is tangential speed, and r is radius.

  • How does centripetal force change if speed doubles?

    Centripetal force increases by a factor of four because force depends on the square of speed.

  • What is centrifugal force in a rotating frame?

    An apparent outward force experienced in a rotating reference frame, equal and opposite to centripetal force.

  • How can centrifugal force simulate gravity in space?

    By spinning a space station, centrifugal force pushes occupants outward, mimicking gravity.

  • State the law of conservation of angular momentum.

    If no external torque acts, the angular momentum of a system remains constant.

  • What happens to angular velocity if rotational inertia halves?

    Angular velocity doubles to conserve angular momentum.