The centripetal force that keeps the beetle moving in circle is given by:
where
m is the mass of the beetle
v is the tangential speed of the beetle
r is the distance of the beetle from the center of the record
In this problem, we know the force (F=0.070 N), the mass of the beetle (m=0.023 kg) and the distance from the center (r=0.15 m), therefore we can re-arrange the equation to find the tangential speed:
When a tree is vigorously shaken, the branches of the tree come in motion but the leaves tend to continue in their state of rest due to inertia of rest. As a result of this, leaves get separated from the branches of the tree and hence fall down.