Best Answer:
I think your lenghts are backwards. From the picture l1 < l2, but in the problem it says l1 > l2. I will go by the picture.

Sum of the moments about the pivot point = I*alpha

Find the moment of inertia:

Treat the blocks as point masses.

I_point mass = m*r^2

I_LHS = m*l1^2

I_RHS = m*l2^2

I_total = I_RHS + I_LHS = m*l1^2 + m*l2^2 = m*(l1^2 + l2^2)

What are the moments? Moments that produce CCW spin will be treated as positive. The mass on the left hand side produces a moment of m*g*l1, which makes the system want to spin CCW (positive). The mass on the right hand side produces a moment of m*g*l2, hich makes the system want to spin CW (negative).

Sum of the moments (CCW = +) = m*g*l1 - m*g*l2 = I_total*alpha

m*g*l1 - m*g*l2 = I_total*alpha

alpha = (m*g*l1 - m*g*l2) / I_total = m*g*(l1 - l2) / (m*(l1^2+l2^2)) = g (l1-l2) / (l1+l2)^2

Plug in numbers, remember to convert cm to m:

alpha = -5.13 rad/s^2

The negative means that the system is going to rotate in the clockwise direction. This means that the LHS is rising.

The tangential/agular acceleration relatonship

a = alpha*r

The radius in this case is l1

a = alpha*l1

Sub in alpha, but since we know it is going up, treat alpha as a positive number so our acceleration will be positive (up).

a = 5.13 rad/s^2 * 0.13 m = 0.667 m/s^2 <--- ANS

Hope I helped explain it.

Source(s):

Asker's rating