Problem 17–67 | Initial Pin Reactions & Angular Acceleration of Beam | Chapter 17 Dynamics

Problem 17–67 | Initial Pin Reactions & Angular Acceleration of Beam | Chapter 17 Dynamics
If the cord at B suddenly fails, determine the horizontal and vertical components of the initial reaction at the pin A, and the angular acceleration of the 120-kg beam. Treat the beam as a uniform slender rod.

In this problem, we analyze the initial motion of a rigid beam after sudden release using the principles of planar rigid body kinetics and Newton–Euler equations of motion.

The solution is presented in a clear, step-by-step manner and includes:

Identifying the geometry and mass properties of the uniform slender beam
Recognizing the sudden loss of support at point B
Drawing the free-body diagram immediately after failure
Locating the center of mass of the beam
Calculating the mass moment of inertia about the pin at A
Applying the rotational equation of motion
∑M
A
​

=I
A
​

α
Determining the initial angular acceleration of the beam
Evaluating the acceleration of the center of mass at the instant of release
Applying Newton’s second law in the horizontal direction
Applying Newton’s second law in the vertical direction
Determining the horizontal reaction component at A
Determining the vertical reaction component at A
Interpreting the initial dynamic response of the beam

This problem is essential for understanding how rigid bodies behave immediately after a constraint is removed and how reactions and angular acceleration develop in transient motion.

This video is especially useful for:

Engineering Mechanics – Dynamics
Rigid Body Kinetics
Initial Motion Analysis
Newton–Euler Equations
Slender Beam Dynamics
Exam and Homework Preparation

Keywords:
engineering mechanics dynamics, rigid body kinetics, beam dynamics problem, sudden release motion, angular acceleration of beam, pin reactions at A, Newton Euler equations, mass moment of inertia, uniform slender rod, chapter 17 dynamics solutions, mechanical engineering dynamics, initial motion analysis, support reaction forces, dynamics problem 17-67, engineering mechanics solved problems, Hibbeler dynamics solutions, rigid body acceleration, general plane motion, exam oriented dynamics problems, transient rigid body motion

Видео Problem 17–67 | Initial Pin Reactions & Angular Acceleration of Beam | Chapter 17 Dynamics канала NUM