Motion of two balls connected by a rod

[mingyz0403]

Homework Statement

A 1-lb ball A and a 2-lb ball B are mounted on a horizontal rod whichrotates freely about a vertical shaft. The balls are held in the positionsshown by pins. The pin holding B is suddenly removed and the ballmoves to position C as the rod rotates. Neglecting friction and the massof the rod and knowing that the initial speed of A is 8 A v = 8 ft/s, determine the radial and transverse components of the acceleration of ball B immediately after the pin is removed

Relevant Equations

F=MA

Since there is no friction, there is no radial force acting on Ball B after the pin is remove. Therefore the radial acceleration of Ball B is zero. I don't know how to determine the transverse components of the acceleration of Ball B. I looked at the textbook solution. It takes moment about the shaft to find the transverse components of the acceleration of ball B. The solution states that " Since the rod is massless, it must be in equilibrium. " Why the rod is massless means it is in equilibrium?

 

[Andrew Mason]

There is no radial force on ball B (until ball B reaches the end at C). Is there any force at all during this time?

Since there is no external torque on the system, what can you say about the angular speed of the rod and ball A after the pin is pulled and B is free to move? What is the angular speed of the rod and A after B hits the end at C? [If no force acts on B during this time, what is B's velocity and what is its angular momentum? Hint: during this time, sinΘ < 1 in L = r x mv = |r|mvsinΘ but |r| is not constant either ]

AM

 

[Andrew Mason]

Just to add a bit more of a hint: B moves at constant velocity after the pin is pulled so it moves tangentially from the point of release until it strikes the stop a C. Its angular momentum with respect to the central point does not change because the cross product r x v remains the same: |r | = |r₀|/sinΘ so |r | sinΘ = |r₀| where r₀ is the radial displacement vector when the pin is pulled.

AM