Call
Angular Motion of a Rod with Beads
(a) Instantaneous Angular Velocity at $ t = 5 $ s:
We'll differentiate the angular position function with respect to time:
\[ \omega = \frac{d\theta}{dt} = \frac{d}{dt} (20.0 t^2) \]
(b) Angular Acceleration:
We'll differentiate the angular velocity function with respect to time:
\[ \alpha = \frac{d\omega}{dt} \]
(c) Tangential Speeds of the Beads at $ t = 5 $ s:
We'll calculate the tangential speeds using the formula:
\[ v = r \omega \]
(d) Tangential Accelerations of the Beads at $ t = 5 $ s:
We'll calculate the tangential accelerations using the formula:
\[ a_t = r \alpha \]
(e) Centripetal Accelerations of the Beads at $ t = 5 $ s:
We'll calculate the centripetal accelerations using the formula:
\[ a_c = \frac{v^2}{r} \]