Angular Acceleration (College Board AP® Physics 1: Algebra-Based)

Angular acceleration

• Angular acceleration is defined as

The change in angular velocity per unit time

• In other words, it describes the rate of change of a system's angular velocity

Average angular acceleration

• The average angular acceleration of a rigid rotating system is defined as:

The average rate at which the angular velocity changes with respect to time

• Average angular acceleration considers the initial and final states of a system over an interval of time

  • In other words, the change in angular velocity over the time interval for which the angular acceleration occurred

• This can be expressed as an equation:

• Where:

  • = average angular acceleration, in

  • = change in angular velocity, in

  • = change in time, in

• This can also be expressed as:

• Where:

  • = final angular velocity, in

  • = initial angular velocity, in

Direction of angular acceleration

• Like linear acceleration, angular acceleration is a vector quantity with both magnitude and direction

• Therefore, an angular acceleration can be due to:

  • a change in the magnitude of a system's angular velocity (i.e. angular speed)

  • a change in the direction of rotation

• Since angular acceleration is a vector quantity, it can have a positive or negative value

• However, the negative or positive value of angular acceleration does not always describe whether the system is rotating faster or slower

  • The sign of an angular position value describes where a point on a system is in relation to the axis of rotation

  • The sign of an angular velocity value describes the direction in which the system is rotating

  • The sign of an angular acceleration value only consistently describes the direction of the angular acceleration vector

• For example, consider a disk rotating about an axis of rotation at its center, where counterclockwise is defined as the positive direction

  • If the disk rotates counterclockwise at a constant rate:

    • its angular speed is unchanged

    • its angular velocity is positive and constant

    • its angular acceleration is zero

  • If the disk is made to spin faster:

    • its angular speed increases

    • its angular velocity is positive and increasing

    • its angular acceleration is positive

  • If the disk is made to spin slower:

    • its angular speed decreases

    • its angular velocity is positive and decreasing

    • its angular acceleration is negative

  • If the disk is made to rotate in the opposite direction (clockwise) at an increasing rate:

    • at the instant the disk changes direction, its angular speed is momentarily zero before it increases

    • its angular velocity is negative and increasing

    • its angular acceleration is negative

Units of angular acceleration

• Angular acceleration is measured in radians per second squared or

  • Since radians can be omitted, it can also be written as

• Angular acceleration does not have any alternative units