- #1

adjurovich

- 119

- 21

Angular displacement is defined as the angle between initial and final radius vector of some arbitrary point on an object undergoing rotation. I’ve seen that some problems include angular displacement bigger than 2 ##\pi## radians. Also, I would note this example:

Let us start with definition of angular velocity:

##\vec{\omega} = \dfrac{d\vec{\theta}}{dt}##

##\int_\vec{\theta_1}^\vec{\theta_2}d \vec{\theta} = \int_{0}^{t} \vec{\omega}dt##

Let’s say that angular velocity is given by linear function: ##\vec{\omega} = \vec{\omega_0} + \vec{\alpha} t##

By integrating, we obtain the final equation:

##\Delta{\vec{\theta}} = \vec{\omega_0}t + \dfrac{1}{2} \vec{\alpha} t^2##

This equation poses no limitations to values of angular position nor angular displacement. Hence it could result in angular displacement bigger than 2 ##\pi## radians. What am I missing?

Let us start with definition of angular velocity:

##\vec{\omega} = \dfrac{d\vec{\theta}}{dt}##

##\int_\vec{\theta_1}^\vec{\theta_2}d \vec{\theta} = \int_{0}^{t} \vec{\omega}dt##

Let’s say that angular velocity is given by linear function: ##\vec{\omega} = \vec{\omega_0} + \vec{\alpha} t##

By integrating, we obtain the final equation:

##\Delta{\vec{\theta}} = \vec{\omega_0}t + \dfrac{1}{2} \vec{\alpha} t^2##

This equation poses no limitations to values of angular position nor angular displacement. Hence it could result in angular displacement bigger than 2 ##\pi## radians. What am I missing?

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