Answer to Question #247864 in Molecular Physics | Thermodynamics for Kelani

Question

The dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigroaeneus has a radius of 1.85 cm and is rolled by the beetle at 6.20 cm/s.

(a)

What is the rolling ball's angular speed (in rad/s)?

___ rad/s

(b)

How many full revolutions are required if the beetle rolls the ball a distance of 1.35 m?

___ rev

Answer 1

First, we use the relation between angular velocity and tangent velocity to find what we're looking for:

$v = \omega r \implies \omega = \cfrac{v}{r}=\cfrac{6.20\frac{cm}{s }}{1.85\,cm} \\ \therefore \omega=3.351\frac{rad}{s}$

Then, for the second part we have to know how much one revolution is:

$1\,revolution=2\pi\,radians = 2\pi r \\ 1\,revolution =(2\pi)(0.0185\,m)=0.037\pi\,[m] \approxeq 0.11624\,m$

Then we use the distance that has to be covered by the rolling ball to know how many revolutions it would take:

$1.35\,m \times \cfrac{1\,revolution}{0.11624\,m} =11.614\,rev \approxeq 12\,rev$

In conclusion, (a) the rolling ball's angular speed is 3.351 rad/s, while (b) we need 12 full revolutions if the beetle rolls the ball through a distance of 1.35 m.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.