Question

Two identical, uniform rods are configured as shown above, and the assemble is released at rest (in the position shown). Find, immediately after release:

$\alpha$_bc (angular acceleration) (magnitude and direction)

a_b (magnitude and direction)

rods 45 Min OX unium and the asbl ured as shown above wo idenicaods are confiq is released at test ántaerosttionshow^1. Find, immediately after elease:

Answer 1

Inertia = I = 1/3 * m*l^2 = 1.8*0.840^2/3 = 0.42 kg m^2

m = mass = 1.8 kg, l = length of the rod = 0.84

Torque = I* alpha

alpha = angular acceleration

Torque = mgx

g = acceleration due to gravity = 9.8 ms^-2

x = perpendicular distance between the line of action and mass

x= l/2 cos (45)= 0.84/2 cos (45) = 0.29 m

Torque = mgx=1.8*9.8*0.29 = 5.11 Nm

alphaBC=angular acceleration of BC = torque/Inertia = 5.11/0.42 = 12.2 rad/s^2 (in the direction perpendicular to the plane of the paper using right hand thumb rule)

aB = linear acceleration = 0 (because the point is not moving)