The figure shows particles 1 and 2, each of mass m , attached to the ends of a r

Question

The figure shows particles 1 and 2, each of mass m, attached to the ends of a rigid massless rod of length L1 + L2, with L1 = 0.90 m and L2 = 7.1 m. The rod is held horizontally on the fulcrum and then released. What are the magnitudes of the initial accelerations of (a) particle 1 and (b) particle 2?

The figure shows particles 1 and 2, each of mass m, attached to the ends of a rigid massless rod of length L1 + L2, with L1 = 0.90 m and L2 = 7.1 m. The rod is held horizontally on the fulcrum and then released. What are the magnitudes of the initial accelerations of (a) particle 1 and (b) particle 2?

Explanation / Answer

torque with respect to the fulcrum point = mgL2 - mgL2

moment of inertia of the system with respect to the fulcrum point = mL1^2 + mL2^2 = I.

I = m(0.9^2 + 7.1^2)

angular acceleration be a.then

I*a = torque

m(0.9^2 + 7.1^2) *a = mg(L2-L1).

51.22*a = 9.8*6.2

a = 1.186 rad/s2.

so intial accelaration of mass at point 1 = a1 = a*L1 =1.186*0.9 = 1.0676 m/s2.--------it is upwards.

acceleration of mass at point 2 = a2 = a*L2 = 1.186*7.1 = 8.4224 m/s2.--------it is downwards.

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