What does Hinge Reaction signify ? How do i calculate it ?

[Sujith Sizon]

I recently came across a lot of problems where components of Hinge Reaction were asked along different axis .

What is hinge reaction ? How do i calculate it ? How do i find its direction ? Does it change angular velocity / acceleration of the body ?Sample Question ) A square lamina of side $a$ is hinged at corner $A$ . An impulse $P_0$ is applied on the lamina as shown . Find the impulse on the hinge due to hinge on the lamina just after $P_0$ is applied ?
http://i.stack.imgur.com/nIAdD.jpg

My attempt-

Angular impulse = Change in angular momentum
$P_{0}a=\frac{2}{3}ma^2 \omega$
$\omega=\frac{3P_0}{2ma}$
Now i found out centripetal force:
$mr {\omega}^2=m\frac{a}{2}{(\frac{3P_0}{2ma})}^{2}$

But the actual answer to the question is $\frac{P_0}{4} \sqrt{10}$. Why doesn't the centrepetal force yield an accurate value for hinge reaction ?

 

[conscience]

I recently came across a lot of problems where components of Hinge Reaction were asked along different axis .

What is hinge reaction ? How do i calculate it ? How do i find its direction ? Does it change angular velocity / acceleration of the body ?Sample Question ) A square lamina of side $a$ is hinged at corner $A$ . An impulse $P_0$ is applied on the lamina as shown . Find the impulse on the hinge due to hinge on the lamina just after $P_0$ is applied ?
http://i.stack.imgur.com/nIAdD.jpg

My attempt-

Angular impulse = Change in angular momentum
$P_{0}a=\frac{2}{3}ma^2 \omega$
$\omega=\frac{3P_0}{2ma}$
Now i found out centripetal force:
$mr {\omega}^2=m\frac{a}{2}{(\frac{3P_0}{2ma})}^{2}$

But the actual answer to the question is $\frac{P_0}{4} \sqrt{10}$. Why doesn't the centrepetal force yield an accurate value for hinge reaction ?

Hello Sujith

I will try to help you with the problem .

As a first step , can you identify the direction of velocity of COM of the square just after the impulse $P_0$ is applied ?