AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 5: Torque & Rotational DynamicsRotational Inertia

Rotational Inertia (College Board AP® Physics 1: Algebra-Based): Flashcards

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  • FrontRotational Inertia

    Define rotational inertia.

Cards in this collection (13)

  • Define rotational inertia.

    Rotational inertia is the resistance to a change of rotational motion, depending on the system's distribution of mass around a chosen axis of rotation.

  • What is the unit of rotational inertia?

    kg·m2

  • State three factors that the rotational inertia of a body depends on.

    • Its shape

    • Its density

    • Its orientation relative to the axis of rotation

  • State the equation for the rotational inertia of a point mass.

    I = mr^{2}

    • I = rotational inertia (kg·m2)

    • m = mass of the object (kg)

    • r = perpendicular distance from the axis of rotation (m)

  • State the equation for the total rotational inertia of a system about an axis.

    I_{\text{tot}} = \underset{i}{\sum} I_{i} = \underset{i}{\sum} m_{i} r_{i}^{2}

    • I_{\text{tot}} = total rotational inertia of the system (kg·m2)

    • I_{i} = rotational inertia of each object about the axis (kg·m2)

    • m_{i} = mass of each object (kg)

    • r_{i} = perpendicular distance of each object from the axis (m)

  • The equation I = mr^{2} applies to objects that can be considered as a ...........

    The equation I = mr^{2} applies to objects that can be considered as a point mass.

  • True or False?

    Two cylinders of the same mass and radius must have the same rotational inertia.

    False.

    A hollow cylinder has more rotational inertia than a solid one, because its mass is distributed further from the axis of rotation.

  • What does the parallel axis theorem allow you to calculate?

    The rotational inertia about an axis that is parallel to an axis passing through the system's center of mass.

  • State the parallel axis theorem.

    I' = I_{cm} + Md^{2}

    • I' = rotational inertia about the parallel axis (kg·m2)

    • I_{cm} = rotational inertia about the axis through the center of mass (kg·m2)

    • M = mass of the system (kg)

    • d = distance between the two axes (m)

  • About which axis is the rotational inertia of a system a minimum?

    The axis that passes through the system's center of mass, compared with any parallel axis.

  • The rotational inertia is the same about any parallel axis at an equal distance from the ...........

    The rotational inertia is the same about any parallel axis at an equal distance from the center of mass.

  • True or False?

    The rotational inertia of a rigid system does not depend on the orientation of its axis.

    False.

    Rotational inertia depends on how the mass is distributed around the axis, so it can change with the orientation of the axis.

  • A thin rod of mass M and length L has I_{cm} = \frac{1}{12}ML^{2}. What is its rotational inertia about one end?

    The axis is a distance d = \frac{L}{2} from the center of mass.

    I' = \frac{1}{12}ML^{2} + M\left(\frac{L}{2}\right)^{2} = \frac{1}{3}ML^{2}

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