What Is Angular Acceleration?
Angular acceleration describes the physical quantity of the rigid body's angular velocity and the rate of change with time. In the International System of Units, the unit is "radian / second squared", usually expressed by the Greek letter .
- Chinese name
- Angular acceleration
- Foreign name
- Angular acceleration
- Unit
- "Radians / second squared"
- Formula
- = / t
- Types of
- Scalar
- Angular acceleration describes the physical quantity of the rigid body's angular velocity and the rate of change with time. In the International System of Units, the unit is "radian / second squared", usually expressed by the Greek letter .
Angular acceleration concept
Average angular acceleration
- The ratio of the angular velocity change of the rotating rigid body from the instant t to the corresponding time interval t is called the average angular acceleration, that is, = / t.
Instantaneous angular acceleration
- If t 0, this ratio is called the angular acceleration of rigid body rotation at instant t, also called instantaneous angular acceleration, and it is recorded as , that is, = lim m) (t 0 = / t = d / dt) .
- When the moment used as an object is constant, the angular acceleration is also constant. In this special case of constant angular acceleration, this equation of motion will calculate a decisive, single-valued angular acceleration.
- When the moment applied to the object is not constant, the angular acceleration of the object will change with time. This equation becomes a differential equation. This differential equation is the equation of motion of the object; it can fully describe the motion of the object.
Angular acceleration calculation formula
- Angular acceleration
- Unit: radians / second ^ 2; (rad / s ^ 2;)
Orientation of angular acceleration
- In plane motion, angular accelerationas the rate of change of angular velocitycan also be similarly defined as a scalar. We can say that a movement is clockwise rotation acceleration or counterclockwise rotation acceleration.
- In real three-dimensional space, the vectority of angular velocity becomes meaningful. Its vector is defined as follows:
- v = × OP (where v, , OP are all vectors, the middle multiplication sign indicates that this is a vector product , not a quantity product)
- Each physical quantity in the above formula should have a vector symbol. Angular acceleration is similar to acceleration, that is, the rate of change of angular velocity. Because the angular velocity is vectorial, the angular acceleration is also vectorial.
- From the kinematics, we can get the magnitude and direction of the angular acceleration by differentiating the above formula.
- That is: a = × OP (where a, , OP are vectors, and here is the vector product)
- Written in scalar form : | a | = | | | OP | sin, that is: | a | = | | r
- In general, we use scalar form for calculation, and vector form is suitable for mathematical derivation.
- If the motion is fixed in a circular motion and r is a constant, then the angular acceleration is equal to | a | / r and the direction is the same as the direction.
- We find that the motion of the two-dimensional plane makes the result of the above vector cross product necessarily in a direction perpendicular to the plane. If the direction of a vector is fixed on a certain line, its performance is indeed very similar to a scalar. [1]