Figure 10-42 shows particles 1 and 2, each of mass m , attached to the ends of a

Question

Figure 10-42 shows particles 1 and 2, each of mass m, attached to the ends of a rigid massless rod of length L1 + L2, with L1 = 1.0 m and L2 = 3.0 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?

Figure 10-42 shows particles 1 and 2, each of mass m, attached to the ends of a rigid massless rod of length L1 + L2, with L1 = 1.0 m and L2 = 3.0 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

{Moment Of Inertia About Fulcrum} = I = m*L1^2 + m*L2^2

{Total Net Torque About Fulcrum} = T = m*g*L1-m*g*L2

{Initial Angular Acceleration} = ? = T/I =
= {m*g*L1-m*g*L2}/{m*L1^2 +m*L2^2}
= {g*L1- g*L2}/{L1^2 + L2^2}
= g*{L1- L2}/{L1^2 + L2^2}
= (9.806)*((1.0) - (4))/((1.0)^2 + (4.0)^2)
= -1.73117647 rad/s/s

(a)----> {InitialAcceleration Magnitude, Object #1} = ?*L1 =
= (1.73117647)*(1.0)
= 1.73117647 m/sec/sec

(b) ---->{Initial Acceleration Magnitude, Object#2} = ?*L2 =
= (1.73117647)*(4.0)
= 6.9247 m/sec/sec

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