ENGR216 2025 Q B1 (ENGR5004)

ENGR216 2025 Q B1Past paperOld spec ENGR2162:125 marks30 min

ENGR216 Summer 2025 Q B1[VALID] official answers

A uniform rod OA with a mass ( $m$ ) and length ( $L$ ) is centrally affixed to a uniform block of mass ( $m$ ). 'O' is the centre of rotation for the rod OA, which is also the centroid of the block, as shown in Figure B1. The block is positioned to move freely along a smooth horizontal surface. Initially, the system is at rest, and the rod OA is oriented horizontally with an initial counterclockwise angular velocity $\omega_{OA}$ .

Figure B1: block of mass m on a smooth floor with rod OA (mass m, length L) pinned at the block centroid O.

Formulas you may need

Relative acceleration (rigid body): $\mathbf{a}_G = \mathbf{a}_O + \boldsymbol\alpha\times\mathbf{r}_{G/O} - \omega^2\mathbf{r}_{G/O}$ (learn this)
Equations of motion: $\sum\mathbf{F} = m\mathbf{a}_G$ , $\sum M_G = I_G\alpha$ ; for a translating body $\sum\mathbf{F} = m\mathbf{a}$ (learn this)
Slender rod about its centre: $I_G = \dfrac{1}{12} m L^2$ (learn this)
Moments about another point P (check): $\sum M_P = I_G\alpha + (\mathbf{r}_{G/P}\times m\mathbf{a}_G)_z$ (learn this)
Newton's third law at a pin: equal and opposite pin forces on the two bodies (learn this)
Friction: static $F \le \mu_s N$ , kinetic $F = \mu_k N$ , opposing the (impending) relative sliding (learn this)

(a)
Draw the free-body and kinetic diagrams of the rod OA and the block. State appropriate coordinate systems.
[10]
(b)
Determine the acceleration of point O on the initial instant.
a_O (towards A +) =omega_OA^2*L
[5]
(c)
Determine the angular acceleration of the rod OA at the instant of (b).
alpha_OA (clockwise +) =g/L
[5]2:2
(d)
If there is friction between the block and the horizontal surface, will the acceleration of point O increase or decrease? Give your reasoning.
[5]