Question

Suppose the rod in the previous problem has a mass of 1 kg distributed uniformly over its length.
(a) Find the initial angular acceleration of the rod.
(b) Find the tension in the supports to the blocks of mass 2 kg and 5 kg.

Answer 1

In this problem the rod has a mass 1 kg

a) πnet = I_net × α
5 × 10 × 10.5 – 2 × 10 × 0.5
= (5 × (1/2)² + 2 × (1/2)² + 1/12) × α

15 = (1.75 + 0.084) α
α = 1500/(175 + 8.4) = 1500/183.4 = 8.1 rad/s² (g = 10)
= 8.01 rad/s² (if g = 9.8)

b) T₁ – m₁g = m₁a
 T₁ = m₁a + m₁g = 2(a + g)
= 2(αr + g) = 2(8 × 0.5 + 9.8)
= 27.6 N on the first body.
In the second body
= m₂g – T₂ = m₂a = T₂ = m₂g – m₂a
= T₂ = 5(g – a) = 5(9.8 – 8 × 0.5) = 29 N.