Free Pivot Rotation: Calculating Kinetic Energy, Angular Speed & Linear Speed

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The discussion revolves around calculating the rotational kinetic energy, angular speed, and linear speed of a system consisting of a cylindrical rod and an attached ball after it pivots. The center of mass was identified as 0.247 meters from the pivot, which is crucial for further calculations. Participants emphasize the importance of showing detailed work to facilitate understanding and problem-solving. The conservation of energy principle is highlighted as a key concept for determining the rotational kinetic energy. Overall, the focus is on applying physics principles to solve interconnected questions regarding the system's dynamics.
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A thin, cylindrical rod = 26.6 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. The combination is free to pivot about the bottom end of the rod after being given a slight nudge.


(a) After the combination rotates through 90 degrees, what is its rotational kinetic energy?

(b) What is the angular speed of the rod and ball?

(c) What is the linear speed of the center of mass of the ball?

so this is the problem and questions for my online physics homework-- the points are soly based on the answers, not the work, and so I'm having trouble finding the answers, since they are all connected.

I think i found the center of mass, being 0.247, and it makes sense. But I'm very unclear how to utilize this.

 
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Welcome to PF. Your value for the position of CM is correct if you meant it in meters. And you should also specify that it is the distance from the pivot.

The custom here is that you show your work in detail, and if you are stuck we help. Question (a) asks about rotational kinetic energy. Remember the law of energy conservation. What does it say?

ehild
 

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