Dynamics L15 Worked example 2 (ENGR5004)

Dynamics L15 Worked example 2TutorialOld spec ENGR2162:212 min

ENGR216 Dynamics L15 worked example 2 (slides 14-16) official answers

A 30 kg solid sphere of radius 0.1 m is fixed to the end of a 10 kg uniform horizontal rod of length 0.2 m, whose other end is pinned to a wall at O (so the sphere's centre is 0.3 m from O). The assembly is held horizontal by a vertical cord AB attached to the top of the sphere. The cord is cut. Take $g = 9.81$ m/s $^2$ , $I_G = \tfrac25 mr^2$ for the sphere and $\tfrac{1}{12}ml^2$ for the rod.

Find the angular acceleration and the reaction at the pin O just after the cord is cut.

Sphere of radius 0.1 m on the end of a 0.2 m horizontal rod pinned to a wall at O; cord AB from the top of the sphere to the ceiling is cut.

Formulas you may need

Fixed-axis rotation: $\sum F_n = m\omega^2 r_G$ , $\sum F_t = m\alpha r_G$ , $\sum M_O = I_O\alpha$ (learn this)
Parallel-axis theorem $I_O = I_G + md^2$ ; sphere $I_G = \tfrac25 mr^2$ , slender rod $I_G = \tfrac{1}{12}ml^2$ (learn this)

I_O =kg m^2

alpha =rad/s^2

O_y (up) =N