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

In summary, a thin, cylindrical rod with a length of 26.6 cm and a mass of 1.20 kg has a ball with a diameter of 10.00 cm and a mass of 2.00 kg attached to one end. The combination is initially vertical and stationary, with the ball at the top. After being given a slight nudge, it is free to pivot about the bottom end of the rod. The questions for this problem involve determining the rotational kinetic energy of the combination after it rotates through 90 degrees, the angular speed of the rod and ball, and the linear speed of the center of mass of the ball. The correct value for the position of the center of mass is 0.247
  • #1
Cupcakes69
1
0
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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  • #2
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
 

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

1. What is free pivot rotation?

Free pivot rotation is a type of motion in which an object is able to rotate around a fixed point without any external force acting on it. This means that the object is not being pushed or pulled by any outside forces, and its motion is solely determined by its own inertia.

2. How is kinetic energy calculated in free pivot rotation?

In free pivot rotation, the kinetic energy of an object is calculated using the equation KE = 1/2 * I * ω², where KE is the kinetic energy, I is the moment of inertia, and ω is the angular speed of the object. This equation relates the object's rotational motion to its kinetic energy, taking into account its mass and how it is distributed around the pivot point.

3. What is angular speed and how is it related to linear speed?

Angular speed is a measure of the rate at which an object rotates around a fixed point. It is usually represented by the symbol ω and is measured in radians per second. Angular speed is related to linear speed through the equation v = r * ω, where v is the linear speed, r is the distance from the pivot point, and ω is the angular speed. This equation shows that as the distance from the pivot point increases, the linear speed also increases for a given angular speed.

4. How does the moment of inertia affect free pivot rotation?

The moment of inertia is a measure of an object's resistance to rotational motion. In free pivot rotation, the moment of inertia is a crucial factor in determining the object's kinetic energy and angular speed. Objects with a larger moment of inertia will require more energy to rotate and will have a lower angular speed compared to objects with a smaller moment of inertia.

5. What are some real-life examples of free pivot rotation?

Some examples of free pivot rotation in everyday life include spinning tops, merry-go-rounds, and figure skaters performing spins. In these cases, the objects are able to rotate freely around a fixed point without any external forces acting on them, demonstrating the principles of free pivot rotation. Similarly, objects such as planets and stars also experience free pivot rotation as they orbit around a fixed point, such as the sun.

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