Rotational Velocity & Acceleration Video Lessons

Concept

# Problem:  An airplane in level flight at an altitude h and a uniform speed u passes directly over a radar tracking station A. Calculate the angular velocity theta and angular acceleration of the radar antenna theta as well as the rate r at which the airplane is moving away from the antenna. Attach the inertial frame of reference to the ground and assume non - rotating earth. Attach the moving frame to the antenna, with the x-axis pointing always from the antenna towards the airplane.

###### FREE Expert Solution

Angular velocity:

$\overline{)\stackrel{\mathbf{.}}{\mathbf{\theta }}{\mathbf{=}}\frac{{\mathbf{v}}_{\mathbf{T}}}{\mathbf{r}}}$, where $\stackrel{\mathbf{.}}{\mathbf{\theta }}$ is the differential of the angular displacement θ with respect to time, vT is tangential velocity, and r is the radius.

Let's consider the diagram:

From the figure:

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###### Problem Details

An airplane in level flight at an altitude h and a uniform speed u passes directly over a radar tracking station A. Calculate the angular velocity theta and angular acceleration of the radar antenna theta as well as the rate r at which the airplane is moving away from the antenna. Attach the inertial frame of reference to the ground and assume non - rotating earth. Attach the moving frame to the antenna, with the x-axis pointing always from the antenna towards the airplane.