Question

The athlete show in figure rotates a 1.00 kg discus along a circular path of radius 1.06 mThe maximum speed of the discus is 20.0 m/s. Determine the magnitude of the maximum radial acceleration of the discus.

Short answer

The maximum radial acceleration of the discus is$377\text{m}/{\text{s}}^2\text{.}$

Step-by-step solution

Identification of the given data

The given data can be listed below as,

The mass of discus is,1.00 kg.

The maximum speed of discus is, 20.0 m/s.

The radius of circular path is, 1.06 m.

The radial acceleration

The radial acceleration is given by:

${\mathit{a}}_{\mathbf{r}}\mathbf{=}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}$

The maximum radial acceleration of the discus

Substitute 20.0 m/s for v and 1.06 m for r in the above equation to find a_r .

$\begin{array}{rcl}{a}_{\text{r}}& =& \frac{{(20.0 \text{m/s})}^2}{1.06 \text{m}}\\ & =& 377.35 {\text{m/s}}^2\\ & \approx & 377 {\text{m/s}}^2\\ & & \end{array}$

Therefore, the maximum radial acceleration of the discus is, $377 {\text{m/s}}^2$.