How Do You Solve the Dynamics of a Mass on a Slope on a Rotating Turntable?

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SUMMARY

The discussion centers on solving the dynamics of a block resting on an inclined plane fixed on a rotating turntable. The key equation derived is the acceleration of the block, expressed as a = -Rω²r̂, where R is the distance from the center of the turntable and ω is the angular velocity. Participants emphasize the importance of drawing a free body diagram to visualize the forces acting on the block and to identify the necessary centripetal force for maintaining circular motion. Additionally, the minimum angular velocity required to prevent the block from sliding down the wedge is a critical aspect of the problem.

PREREQUISITES
  • Cylindrical coordinates in physics
  • Understanding of centripetal force
  • Static friction concepts
  • Free body diagram techniques
NEXT STEPS
  • Study the principles of centripetal acceleration in rotating systems
  • Learn how to construct and analyze free body diagrams
  • Explore static friction and its role in inclined planes
  • Investigate angular velocity calculations in rotational dynamics
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Students studying physics, particularly those focusing on dynamics and rotational motion, as well as educators looking for examples of real-world applications of these concepts.

Ciaran
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Homework Statement


A wedge with face inclined at an angle theta to the horizontal is fixed on a rotating turntable. A block of mass m rests on the inclined plane and the coefficient of static friction between the block and the wedge is μ. The block is to remain at position R from the centre of the turntable. Show that the acceleration is a=-Rω^(2)r̂ .Find the components of the block's acceleration parallel and vertical to the inclined plane. Finally, find the minimum angular velocity needed to keep the block from sliding down the face of the wedge

Homework Equations


a=-Rω^(2)r̂
3. The Attempt at a Solution
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I'm really not sure how to start this problem- I know I need to use cylindrical coordinates with z constant but apart from that, I'm really stuck. Any help would be much appreciated!
 
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Start off with a free body diagram, indicate and observe all the forces acting on the body,
 
Hello Ciaran, a belated welcome to PF :smile: !

I see you started two other threads earlier on and haven't been house trained wrt the funny habits on PF. Please check the guidelines ! At least this time there is an equation, but your attempt at solution isn't up to snuff.

Nevertheless: A drawing helps, and once you realize the block makes a circular trajectory, things will fall into place very nicely: for such a trajectory the resultant of all forces has to be a centripetal force ma with a as you state in the problem statement. You can draw all applicable forces and add them.
 

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