Question

Suppose the rod in the previous problem has a mass of 1 kg distributed uniformly over its length.

(a) Find the initial angular acceleration of the rod.

(b) Find the tension in the supports to the blocks of mass 2 kg and 5 kg.

Answer 1

In this problem the rod has a mass 1 kg

(a) ${\tau }_{net}=I_{net}\times \alpha$

$\Rightarrow 15=(1.75+0.084)\alpha$

$\Rightarrow \alpha =\frac{1500}{(175+8.4)}$

= $\frac{1500}{183.4}$

$=8.1{\text{rad/s}}^2(g=10)$

$=8.01{\text{rad/s}}^2\left(\text{if g =}9.8\right)$

(b) ${\text{T}}_1-m_{1}g=m_{1}a$

$\Rightarrow T_1=m_{1}a+m_{1}g$

$=2(a+g)=2(\alpha r+g)$

$=2(8\times 0.5+9.8)$

$=2\times 13.8$

$=27.6\text{N on the first body}$

$\text{In the second body}$

$\Rightarrow m_{2}g-T_2=m_{2}a$

$\Rightarrow T_2=m_{2}g-m_{2}a=5(g-a)$

$=5(9.8-8\times 0.5)$

$=5\times 5.8=29\text{N}$