A massless beam is supported only at one point, called the pivot point, as shown

Question

A massless beam is supported only at one point, called the pivot point, as shown in the diagram. A block with mass m1 sits at the left end of the beam, a distance L1 from the pivot point. A block with mass m2 sits at the right end of the beam, a distance L2 from the pivot point. L2 > L1. Calculate all torques about the pivot point, remembering that positive is anti-clockwise.
Select Yes, No, Less than, Equal to, or Cannot tell.

1) Given particular values of m1, m2, and L1, is it always possible to choose L2 (with L2 > L1) such that the masses have no angular acceleration?

2) Given particular values of L1 and L2, does the angular acceleration depend only on m1 / m2 ? (If it depends on the actual values of m1 and m2, put 'no'.)

3) If m1 * L1 = m2 * L2, is there a net (non-zero) torque?

4) If m1 = m2, will the masses have an angular acceleration?

Explanation / Answer

Torques: -m2*L2 and m1*L1 1)YES...No angular acc. implies no net torque...implies m1*L1 = m2*L2 ; m2 =m1*L1/L2. 2) NO....given L1,L2 angular acceleration depends on net torque '-m2*L2 + m1*L1'...and it does not depend on m1/m2 only. 3) No...there is no net torque. m1*L1 = m2*L2 is the torque balance equation. 4)YES... if m1 = m2 ,Net torque = -m2*L2 + m1*L1 = m1(L1-L2) is not equal to zero as L2>L1.Hence there is net torque and so is acceleration.

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