The100-kg pendulum has a center of mass at G and a radius of gyration about G of kg = 250 mm. Determine the horizontal and vertical components of reaction on the beam by the pin A and the normal reaction of the roller B at the instant 6 = 07 when the pendulum isrotating at @ = 4 rad/s. Neglect the weight of the beam and the support.

The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. Ignore the spring's mass. (5)  At state 2, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places) (6) The elastic potential energy of the spring at the state 2 is_______(N·m) (two decimal places)  (7) The instantaneous center of zero velocity (IC) of the wheel at state 1 is (8) The mass moment of inertial of the wheel about its mass center G is IG =_________(kg·m2 ) (two decimal places)

The mobile crane is symmetrically supported by two outriggers at A and two at B to relieve the suspension of the truck upon which it rests and to provide greater stability. If the truck, crane, and counter-weight have a total mass of 18-tonnes and center of mass at G1, while the boom has a mass of 1.8-tonnes and a center of mass at G2, determine the critical angle where tipping starts to occur when the boom is supporting a load having a mass of 3-tonnes. Plot the total reactions at A and B (in kN) as functions of θ from θ=0° to the critical angle.

SOLVE USING PRINCIPLE OF WORK AND ENERGY