NOTE: The view of the figure provided is that of the rod as seen from above the surface on which the rod lies. Gravity is directed into the screen.

DISCUSSION
This is a straight-forward application of the Newton-Euler equations to a single rigid body moving in a plane. Consider the four-step plan:

1. FBD: Only a single force acting on the body in its plane of motion.

2. Newton/Euler: Use the two components of the Newton equations and one Euler equation for the rigid body:
∑F_x = … = m*a_Gx
∑F_y = … = m*a_Gy
∑M_G = … = I_G*α

3. Kinematics: None needed here.

4. Solve

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Discussion and hints:

Recall the following four-step plan outline in the lecture book and discussed in lecture:

Step 1: FBDs
Draw a free body diagram of the bar.

Step 2: Kinetics (Newton/Euler)
Write down the Newton/Euler equations for the bar using your FBD above. Take care in choosing the reference point for your moment equation. In order to use the “short form” of Euler’s equation, this point should be either a fixed point or the body’s center of mass. For this problem, there are no fixed points.

Step 3: Kinematics
The paths of A and B are known: A travels on a straight path aligned with the inclined wall, and B travels on a circular path centered at O. Since the bar is released from rest, you know that the speeds of A and B are zero – therefore, the centripetal component of acceleration for each point is zero. This leaves the acceleration of points A and B tangent to their paths. (You can see this from the animation above for the instant when AB is horizontal.) It is recommended that you use two kinematics equations: one relating points A and B, and the other relating the center of mass G of the bar to either A or B.

Step 4: Solve
Solve your equations above for the tension in cable BO.

Any questions?

Any questions?? Please ask/answer questions regarding this homework problem through the “Leave a Comment” link above.

DISCUSSION
Using the four-step plan:

STEP 1: Free body diagram (FBD) – Draw an FBD of bar AB.

STEP 2: Kinetics – Write down the Newton/Euler equations for the bar based on your FBD above. For the “short form” of the Euler equation, please note that you are constrained to using a moment about the center of mass G since there are no fixed points on AB; that is, you should use ΣM_G = I_G α.

STEP 3: Kinematics – With the inextensible cable being taut, all points on the rigid body AB have the same acceleration, and the angular acceleration of AB is zero: α = 0.

STEP 4: Solve – Use the equations from STEPS 2 and 3 to solve for the tension in the cable and the reaction at on the bar at A.

Any questions?? Please ask/answer questions regarding this homework problem through the “Leave a Comment” link above.