Unable to solve rotation KE problem using torque

[Zynoakib]

Homework Statement

A war-wolf or trebuchet is a device used during the Middle
Ages to throw rocks at castles and now sometimes
used to fling large vegetables and pianos as a sport. Model it
as a stiff rod of negligible mass, 3.00 m long, joining
particles of mass m1 = 0.120 kg and m2= 60.0 kg at its
ends. It can turn on a frictionless, horizontal axle perpendicular
to the rod and 14.0 cm from the large-mass
particle. The operator releases the trebuchet from rest
in a horizontal orientation. Find the maximum
speed that the small-mass object attains.

Homework Equations

The Attempt at a Solution

I could get the answer using rotational KE concept but when do the same thing with torque, I cannot get the answer.

Net torque = (60)(9.8)(0.14) - (0.12)(9.8)(2.86) = 78.96 Nm

Find the moment of inertia of the system

Center of mass of the system: [(0.12)(0) + (60)(3)]/ 60.12 = 2.994 m

Moment of inertia at CM
(0.12)(2.994)^2 + (60)(3 - 2.944)^2 = 1.078 kgm^2

Moment of inertia = Moment of inertia at CM + MD^2 = 1.078 + (60 + 0.12)(2.994 - 2.86)^2 = 2.158 kgm^2

Net torque = moment of inertia x angular acceleration
78.96 = 2.158 x acceleration
acceleration = 36.6 rads^-2

s = 1.57 rad, a = 36.6, u = 0, v = ?
v = 10.7 rad/s = 30.66 m/s, which is wrong

Is that because the downward force by weight is not constant during the rotation, so that the torque and the angular acceleration I calculated will become wrong as they way I calculated it seems to treat everything to be constant during the rotation

Thanks!

 

[ehild]

No, the torque is not constant during the motion. How do you calculate the torque?