Question

the athlete shown in figure p4.21 rotates a 1.00-kg discus along a circular path of radius 1.06 m. the maximum speed of the discus is 20.0 m/s. determine the magnitude of the maximum radial acceleration of the discus.

Explanation:

Step1: Recall radial acceleration formula

The formula for radial (centripetal) acceleration is $a_r = \frac{v^2}{r}$, where $v$ is the linear speed and $r$ is the radius of the circular path.

Step2: Substitute given values

Substitute $v = 20.0\ \text{m/s}$ and $r = 1.06\ \text{m}$ into the formula:
$a_r = \frac{(20.0)^2}{1.06}$

Step3: Calculate the result

First compute $(20.0)^2 = 400$, then divide by 1.06:
$a_r = \frac{400}{1.06} \approx 377.36$

Answer:

$\approx 377\ \text{m/s}^2$ (or $377.36\ \text{m/s}^2$ for more precision)