Part 1#

In brachiation, monkeys move from tree branch to tree branch by swinging from their arms. In the position shown in the figure (left), draw a free body diagram on the provided axes in the figure (right) for the monkey, assuming that it is momentarily at rest. (Label the forces $\overrightarrow{F}$ and $\overrightarrow{W}$ with subscripts on each, and include the angle).

Let the mass of the monkey be 10 kg, $\theta$ = 30 ${}^{\circ }$ , and the centre of mass of the monkey to be 50 cm from its centre of mass as shown in the figure.

Part 2#

Calculate the torque exerted by $\overrightarrow{F\mathrm{\_}monb}$ about the branch.

Part 3#

Calculate the torque exerted by the mass of the monkey about the branch.

Part 4#

The moment of inertia of a solid sphere about its centre is $\frac{2}{5}$ $M$$R^2$ . If the the mass of the monkey can be treated as a sphere of radius 30 cm. Find the moment of inertia of the monkey about its centre.

Part 5#

The parallel axis theorem states that moment of inertia of an object of mass $m$ about an axis, a distance $d$ from its centre of mass is given by $I$ = $I\mathrm{\_}cm$ + $m$$d^2$ . Find the moment of inertia of the spherical monkey about the branch.

Part 6#

Find the angular acceleration of the monkey.

Part 7#

Find the tangential acceleration of the centre of mass of the monkey about the branch.

Part 8#

Your result from part 7 is not the same as you would get from solving for the acceleration from the free body diagram in part 1. Explain why this is, referring to the particle model.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.