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

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

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  • FrontRotating Systems

    Define rigid system.

Cards in this collection (52)

  • Define rigid system.

    A rigid system is a system that does not change shape, but different points within the system may move in different directions and with different speeds.

  • How are objects modeled in linear and in rotational motion?

    • Linear motion: point particles, with all the mass at a single point and size and shape ignored

    • Rotational motion: rigid, extended bodies, with the mass distributed throughout and size and shape not ignored

  • Which quantities describe the rotation of a rigid system?

    • Angular displacement

    • Angular velocity

    • Angular acceleration

  • When can a rotating system be treated as a single object?

    When its rotation about an axis can be described by the displacement, velocity and acceleration of its center of mass.

  • Calculations involving rotating systems can be simplified by considering the motion of the system's ...........

    Calculations involving rotating systems can be simplified by considering the motion of the system's center of mass.

  • True or False?

    If the Sun's gravity stopped acting, Earth would stop rotating on its axis.

    False.

    The gravitational force acts at Earth's center of mass and does not affect its rotational motion, so Earth would keep rotating but stop revolving around the Sun.

  • Define angular position.

    Angular position is the rotational location (angle) of a point on a rigid system, relative to a reference point.

  • Define angular displacement.

    Angular displacement is the change in angle through which a point on a rigid system rotates about a specified axis.

  • State the equation for angular displacement.

    ∆\theta = \theta - \theta_{0}

    • ∆\theta = angular displacement (rad)

    • \theta = final angular position (rad)

    • \theta_{0} = initial angular position (rad)

  • Define radian.

    A radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

    \theta = \frac{s}{r}

  • How do you convert an angle from degrees to radians?

    \theta_{\text{rad}} = \theta_{°} \times \frac{\pi}{180°}

  • If counterclockwise is defined as positive, what is the sign of the angular displacement for a clockwise rotation?

    It is negative. Either direction can be positive only if the opposite direction is negative.

  • One complete revolution (360°) is equivalent to .......... radians.

    One complete revolution (360°) is equivalent to 2π radians.

  • True or False?

    Angular displacement is a scalar quantity.

    False.

    Angular displacement is a vector quantity with both magnitude and direction (clockwise or counterclockwise).

  • Define angular speed.

    Angular speed is the change in angular position per unit time.

  • Define average angular velocity.

    Average angular velocity is the average rate at which angular position changes with respect to time.

  • State the equation for average angular velocity.

    \omega_{\text{avg}} = \frac{∆\theta}{∆t}

    • \omega_{\text{avg}} = average angular velocity (rad/s)

    • ∆\theta = angular displacement (rad)

    • ∆t = time interval (s)

  • If counterclockwise is positive, what does a negative angular velocity indicate?

    The system is rotating clockwise.

  • What are the units of angular velocity?

    • radians per second (rad/s), which can also be written as 1/s

    • revolutions per minute (rpm) is also sometimes used

  • How do you convert rpm to rad/s?

    \omega \text{ (rad/s)} = \omega \text{ (rpm)} \times \frac{2\pi \text{ rad}}{60 \text{ s}}

  • Angular velocity acts in the same direction as angular ...........

    Angular velocity acts in the same direction as angular displacement.

  • True or False?

    An angular velocity of 1 rpm is equal to 1 rad/s.

    False.

    One revolution is 2π rad and one minute is 60 s, so 1 rpm = 2π/60 rad/s, which is about 0.105 rad/s.

  • Define angular acceleration.

    Angular acceleration is the change in angular velocity per unit time.

  • State the equation for average angular acceleration.

    \alpha_{\text{avg}} = \frac{∆\omega}{∆t} = \frac{\omega - \omega_{0}}{∆t}

    • \alpha_{\text{avg}} = average angular acceleration (rad/s2)

    • ∆\omega = change in angular velocity (rad/s)

    • ∆t = time interval (s)

    • \omega = final angular velocity (rad/s)

    • \omega_{0} = initial angular velocity (rad/s)

  • What are the units of angular acceleration?

    radians per second squared (rad/s2), which can also be written as 1/s2

  • What two changes can produce an angular acceleration?

    • A change in the magnitude of the angular velocity (the angular speed)

    • A change in the direction of rotation

  • What is the angular acceleration of a system rotating at a constant angular velocity?

    It is zero, because the angular velocity is not changing.

  • Angular acceleration is a .......... quantity with both magnitude and direction.

    Angular acceleration is a vector quantity with both magnitude and direction.

  • True or False?

    A negative angular acceleration always means the system is slowing down.

    False.

    The sign only describes the direction of the angular acceleration vector. A system rotating clockwise (negative) and speeding up has a negative angular acceleration.

  • State the equation linking linear distance and angular displacement.

    ∆s = r∆\theta

    • ∆s = linear distance traveled by the point (m)

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

    • ∆\theta = angular displacement (rad)

  • State the equation linking linear speed and angular speed.

    v = r\omega

    • v = linear speed of a point (m/s)

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

    • \omega = angular speed of the system (rad/s)

  • State the equation linking tangential acceleration and angular acceleration.

    a_{T} = r\alpha

    • a_{T} = tangential acceleration of a point (m/s2)

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

    • \alpha = angular acceleration of the system (rad/s2)

  • Define tangential velocity.

    Tangential velocity is the linear velocity of a point on a rotating rigid body. Its instantaneous direction is always at a tangent to the point's circular path.

  • How does the linear velocity of a point on a rotating rigid body vary with distance from the axis?

    • It increases with distance from the axis

    • It has a maximum value at the radius of the system

    • It is zero at the axis of rotation

  • Which quantities are the same for every point on a rotating rigid system?

    • Angular velocity

    • Angular acceleration

  • The .......... acceleration of a point on a rotating rigid body is the rate of change of its linear velocity.

    The tangential acceleration of a point on a rotating rigid body is the rate of change of its linear velocity.

  • True or False?

    Two points at different distances from the axis of a rotating rigid body have the same linear speed.

    False.

    They have the same angular speed, but since v = r\omega the point farther from the axis has the greater linear speed.

  • State the rotational kinematic equation used when angular displacement is not required.

    \omega = \omega_{0} + \alpha t

    • \omega = final angular velocity (rad/s)

    • \omega_{0} = initial angular velocity (rad/s)

    • \alpha = angular acceleration (rad/s2)

    • t = time interval (s)

  • State the rotational kinematic equation used when final angular velocity is not required.

    \theta = \theta_{0} + \omega_{0}t + \frac{1}{2}\alpha t^{2}

    • \theta = final angular position (rad)

    • \theta_{0} = initial angular position (rad)

    • \omega_{0} = initial angular velocity (rad/s)

    • \alpha = angular acceleration (rad/s2)

    • t = time interval (s)

  • State the rotational kinematic equation used when time is not required.

    \omega^{2} = \omega_{0}^{2} + 2\alpha(\theta - \theta_{0})

    • \omega = final angular velocity (rad/s)

    • \omega_{0} = initial angular velocity (rad/s)

    • \alpha = angular acceleration (rad/s2)

    • \theta - \theta_{0} = angular displacement (rad)

  • State the rotational kinematic equation used when angular acceleration is not required.

    ∆\theta = \frac{1}{2}(\omega_{0} + \omega)t

    • ∆\theta = angular displacement (rad)

    • \omega_{0} = initial angular velocity (rad/s)

    • \omega = final angular velocity (rad/s)

    • t = time interval (s)

  • State the rotational kinematic equation used when initial angular velocity is not required.

    \theta = \theta_{0} + \omega t - \frac{1}{2}\alpha t^{2}

    • \theta = final angular position (rad)

    • \theta_{0} = initial angular position (rad)

    • \omega = final angular velocity (rad/s)

    • \alpha = angular acceleration (rad/s2)

    • t = time interval (s)

  • Why can the time interval be written as t in the rotational kinematic equations?

    The timer is assumed to start from zero (t_{0} = 0), so ∆t = t.

  • The rotational kinematic equations are the rotational analogs of the .......... kinematic equations.

    The rotational kinematic equations are the rotational analogs of the linear kinematic equations.

  • True or False?

    The rotational kinematic equations apply even when angular acceleration changes.

    False.

    The equations only apply when the angular acceleration is constant.

  • What do the slope, area and y-intercept represent on an angular position-versus-time graph?

    • Slope: angular velocity

    • Area under the curve: nothing

    • y-intercept: initial angular position

  • What do the slope and area represent on an angular velocity-versus-time graph?

    • Slope: angular acceleration

    • Area under the curve: angular displacement

  • What does a zero slope represent on an angular position-versus-time graph?

    A state of rest (no rotation).

  • What does a curved line represent on an angular position-versus-time graph?

    An angular acceleration, because the angular velocity (the slope) is changing.

  • What does a curve represent on an angular velocity-versus-time graph?

    Non-constant angular acceleration.

  • The area under an angular acceleration-versus-time graph equals the change in angular ...........

    The area under an angular acceleration-versus-time graph equals the change in angular velocity.

  • True or False?

    A horizontal line on an angular velocity-versus-time graph means the system is at rest.

    False.

    A horizontal line has zero slope, so the angular acceleration is zero and the system rotates with a constant angular velocity. It is at rest only if the line lies along the time axis.

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