When the particle rotates around an axis, the angular velocity may also change with time.We call the change of angular velocity per unit time angular acceleration[1]。
Angular acceleration describes the physical quantity of angular velocity change speed and direction.If the angular velocity of an object changes, it is said that the object has angular acceleration[5]。Set toneThe angular velocity of the rigid body at that moment is ωone, the angular velocity of the rigid body becomes ω after Δ t timetwo, then the average angular acceleration of the rigid body rotating with fixed axis in Δ t time is[3]
The instantaneous angular acceleration of Δ t → 0 is[3]
Angular acceleration meaning
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What does angular acceleration mean?Imagine a stationary merry go round.Because it is not rotating, its angular velocity is zero.Now you start it and make it rotate at a speed of 1 revolution every 4 seconds, that is, 0.25 r/s.So the angular speed of the merry go round becomes non-zero.If the rotation speed is kept constant, then its angular acceleration is zero[4]。
Direction of angular acceleration
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We can use positive and negative signs to indicate the direction of angular velocity and angular acceleration. If the direction of the agreed angular velocity and angular acceleration is parallel to the direction of the rotation axis, the sign is positive, and if the direction is reverse parallel, the sign is negative[1]。
Acceleration and angular acceleration
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Acceleration is the change of velocity, so the unit of angular acceleration is radians per second.Similarly, because radians are dimensionless, the unit of angular acceleration can be written as 1/stwo。In all these respects, angular motion and linear motion can correspond in parallel.The speed is equal to the change of position divided by the change of time. Similarly, the angular speed is equal to the change of angular position divided by the change of time[4]。
Angular acceleration describes the physical quantity of angular velocity change speed and direction.If the angular velocity of an object changes, it is said that the object has angular acceleration[5]。
Dynamic cone angular acceleration β
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The instantaneous angular acceleration of a moving cone is defined as the derivative of the instantaneous angular velocity with respect to time[6]。
