Question

A discus thrower (Fig. P4.33, page 104) accelerates a discus from rest to a speed of 25.0 m/s by whirling it through 1.25 rev. Assume the discus moves on the arc of a circle 1.00 m in radius. (a) Calculate the final angular speed of the discus. (b) Determine the magnitude of the angular acceleration of the discus, assuming it to be constant. (c) Calculate the time interval required for the discus to accelerate from rest to 25.0 m/s.

Short answer

The final angular speed of discus is $25rad/s$.

Step-by-step solution

Identification of given data

The initial speed of discus is $u=0m/s$

The initial speed of discus is $v=25m/s$

The radius of arc of circle is $r=1m$

Conceptual Explanation

The angular speed of an object is the variation in the angular displacement of the object with time. The final angular speed of the discus is found using the relation between the linear speed $\left(v\right)$and angular speed $\left(\omega \right)$.

$\mathit{v}\mathbf{=}\mathit{r}\mathbf{\times }\mathit{\omega }$

Here, r is the radius of the circular path.

Determination of final angular speed of the discus

The final angular speed of discus is given as:

$v=r·\omega$

For $r=1m$ and $v=25m/s$, the above equation gives-

$$\begin{gathered} 25m/s=\left(1m\right)\omega \\ \omega =25rad/s \end{gathered}$$

Therefore, the final angular speed of discus is $25rad/s$.