Are angular & vertical velocity the same if the objects are connected

In summary, the conversation discusses the relationship between angular and linear velocity in an engine with a flywheel and connected rod. When the engine is in equilibrium, the hanged object remains at the same height. However, as the engine starts to rotate, the rod also rotates and causes the hanged object to move downwards while the string becomes loose. The question being posed is whether the vertical velocity of the hanged mass is equal to the angular velocity of the flywheel. It is important to note that this relationship is further illustrated through a diagram on the website provided.
  • #1
Isolde Wilde
6
0
think of a engine. it has a flywheel and a rod connected to it. a string had been totally wrapped around the rod and a mass is hanged from the very end of the rod. the system is in equilibrium. but as the engine starts to rotate, the rod with rotate as well and cause the hanged object to go down while the string comes lose as the rod rotates. is the vertical velocity of the mass hanged equal to the angular velocity of the flywheel?
 
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  • #2
What is the relationship between angular and linear velocity? You are leaving off an important term so far...

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/avel.gif

avel.gif
 

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1. Are angular and vertical velocity the same?

No, angular and vertical velocity are not the same. Angular velocity refers to the rate of change of an object's angular position, while vertical velocity refers to the rate of change of an object's vertical position.

2. Can objects connected by a string have different angular and vertical velocities?

Yes, objects connected by a string can have different angular and vertical velocities. This is because the string can allow for independent movement in the horizontal and vertical directions.

3. How are angular and vertical velocities related?

Angular and vertical velocities are related through the concept of tangential velocity. Tangential velocity is the component of velocity that is perpendicular to the radius of rotation, and it is equal to the product of angular velocity and the distance from the center of rotation.

4. Is there a formula for calculating angular and vertical velocities?

Yes, the formula for calculating angular and vertical velocities is v = ωr, where v is tangential velocity, ω is angular velocity, and r is the distance from the center of rotation.

5. Can the angular and vertical velocities of an object change over time?

Yes, the angular and vertical velocities of an object can change over time. This can happen if there is a change in the object's angular or vertical position, or if there is a change in the object's radius of rotation.

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