4. A uniform bar AB of mass m and length 2a is supported from a single point O by two light threads OA and OB each of length a √ 2 as shown in Figure 4. The bar is initially at rest. The thread OB is cut and the bar is free to move under the influence of gravity. Its position depends on the rotation θ of the thread OA and ϕ of the bar as indicated in Figure 4. Immediately after the thread OB is cut: a) find the i and j components of the acceleration of G, the centre of the bar, in terms of

a, θ and ϕ and their time derivatives;

[6 marks]

b) find the angular acceleration of the bar AB and find also the tension in thread OA; and,

[5 marks]

c) show that the acceleration of point C (midway between G and B) is

a ¨θi − a( ¨θ + 3 2 ϕ¨)j .

Note: The mass moment of inertia of a uniform bar of length 2a and mass m about its centroidal axis is 1 3 ma2 . Ignore the mass of the threads since they are light.

Answer rating: 100% (QA)

a The i and j components of the acceleration of G ... View the full answer