Deriving RPM for Object Slipping from Rotating Surface

In summary, the conversation discusses a scenario where a rotating surface reaches a critical speed and causes an object placed on it to slip. The task is to derive an expression for the number of rotations per minute that the surface makes at this critical time. The key factors to consider are the forces acting on the object and the direction of rotation.
  • #1
icanletyougo
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Homework Statement



A object(have mass M1) is placed at a R1 distance from the center of a horizontal surface that can rotate. The surface rotation is very FAST INCREASE ( tangential acceleration is non-negligible) until the surface reaches a cirtical rotation rate. At that instant, the object begins to slip with respect to the surface. Derive an expression for number of rotation per minute made by the surface at this critical time.
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Homework Equations


The Attempt at a Solution


I have no idea...Can somebody give my a hint? thank you
 
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  • #2
What holds the block in place? What forces are operating? What are their directions?
 

1. What is the purpose of deriving RPM for object slipping from a rotating surface?

The purpose of deriving RPM (rotations per minute) for object slipping from a rotating surface is to calculate the speed at which an object is rotating on the surface. This information can be useful in a variety of scientific fields, such as physics, engineering, and mechanics.

2. How is RPM calculated for an object slipping from a rotating surface?

RPM is calculated by dividing the linear speed of the object by the circumference of the rotating surface. This can be represented by the formula: RPM = v/(2πr), where v is the linear speed and r is the radius of the rotating surface.

3. What factors can affect the RPM of an object slipping from a rotating surface?

There are several factors that can affect the RPM of an object slipping from a rotating surface. These include the radius of the surface, the friction between the object and the surface, the weight of the object, and the force applied to the object.

4. How can the calculated RPM be used in real-world applications?

The calculated RPM can be used in a variety of real-world applications, such as designing and testing machinery, determining the speed of a rotating object, and analyzing the performance of vehicles and engines.

5. Are there any limitations to using RPM to measure the speed of an object slipping from a rotating surface?

Yes, there are limitations to using RPM to measure the speed of an object slipping from a rotating surface. This method assumes that the object is slipping at a constant speed and does not take into account any changes in speed or direction. Additionally, it may not be accurate for objects with irregular shapes or surfaces.

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