Rotational kinematic equations:

$\overline{){{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{\alpha}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{(}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{)}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\alpha}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{\mathbf{\omega}}}_{{\mathbf{f}}}^{{\mathbf{2}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\alpha}}{\mathbf{\u2206}}{\mathbf{\theta}}}$

**(a)**

Centripetal acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{\mathbf{r}}{{\mathbf{\omega}}}^{{\mathbf{2}}}}$

Using the first rotational kinematic equation:

ω(t) = ω_{0} + αt

A rotating platform of radius R = 4.5 cm starts from rest and accelerates with uniform angular acceleration α = 42 rad/s^{2}.

Part (a). Write an expression that gives the centripetal acceleration on the edge of the platform as a function of time a_{c}(t).

Part (b). Write an expression for the time at which the magnitudes of the centripetal and tangential accelerations at the edge will be equal.

Part (c). Calculate the time, in seconds, for when the magnitudes of the centripetal and tangential accelerations are equal.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Types of Acceleration in Rotation concept. You can view video lessons to learn Types of Acceleration in Rotation. Or if you need more Types of Acceleration in Rotation practice, you can also practice Types of Acceleration in Rotation practice problems.