Classical Mechanics-Moments of Inertia and Torques

[sclatters]

Homework Statement

a)Two people are holding the ends of a plank of length l and mass M. Show that, if one suddenly let's go, the initial acceleration of the free end (a_D) is 3g/2. (7 marks).



Moment of inertia, I, of the plank about its centre of mass is given by I=1/12(Ml²)

b)Show also that the load supported by the other person falls from Mg/2 to Mg/4. (3 Marks).

Homework Equations

I*angular acceleration=torque=rxF

parallel axis theorem for the moment of inertia

The Attempt at a Solution

I have completed the first 7 marks with no difficulty but am really struggling with how to set part b) up and what assumptions I need to make. I've spent hours and hours on this and have ended up going round in circles.

I think I may need to calculate the linear acceleration of the centre of the plank and from this deduce the new load on the other hand. However I have not made much progress with this part of the question.

 

[Doc Al]

I think I may need to calculate the linear acceleration of the centre of the plank and from this deduce the new load on the other hand.

That's exactly what you have to do. What forces act on the body? Apply Newton's 2nd law.

 

[sclatters]

So I need to calculate the linear acceleration of the centre of the plank then apply Newtons 2nd law to this? This would give the net force on the plank? After this I could deduce that the the net force=mg-(the load on the other hand? Would this work?

 

[Doc Al]

So I need to calculate the linear acceleration of the centre of the plank then apply Newtons 2nd law to this? This would give the net force on the plank? After this I could deduce that the the net force=mg-(the load on the other hand? Would this work?

You got it.