The real challenge was the . It was attached to the moving boom, meaning it was translating and rotating simultaneously— General Plane Motion .
ω=vArA/IC=vBrB/IComega equals the fraction with numerator v sub cap A and denominator r sub cap A / cap I cap C end-sub end-fraction equals the fraction with numerator v sub cap B and denominator r sub cap B / cap I cap C end-sub end-fraction Once you calculate , you can find the velocity of any other point on the body using 3. Acceleration Analysis (Relative Acceleration)
The velocity of point A is given by: v_A = v_G + ω × r_A
omega equals the fraction with numerator d theta and denominator d t end-fraction Angular Acceleration ( The rate of change of angular velocity. Hibbeler Dynamics Chapter 16 Solutions
Since the angular velocity is constant, α = 0.
This is the heart of Chapter 16 and typically where students seek solutions. It describes the motion of a point relative to a known base point
In this motion, all particles of the rigid body move in circular paths about a fixed axis. The angular position ( ), angular velocity ( ), and angular acceleration ( ) govern the entire system. (directed tangent to the circular path). The real challenge was the
) using geometry. By taking the first and second time derivatives, you can solve for velocity ( ) and acceleration ( 3. Relative-Velocity Analysis Using the vector equation
4. Relative Motion Analysis: Velocity (Sections 16.5 & 16.6)
In translation, every point on the rigid body moves along parallel paths. It describes the motion of a point relative
Before jumping into the numbers, it is critical to identify the type of motion a rigid body is undergoing. In Chapter 16, all analysis is limited to —meaning the movement occurs within a single 2D plane. Here are the three primary categories:
Write a geometric equation relating the position coordinates, then differentiate it with respect to time to find velocities and accelerations. 4. Relative-Motion Analysis (Velocity and Acceleration)
Does the method match your intuition? If not, re-read the problem statement.