How do different forces affect the acceleration of a spinning uniform disk?

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SUMMARY

The discussion clarifies the distinction between center of mass acceleration and angular acceleration in the context of a spinning uniform disk. When a force is applied to initiate spinning, the angular acceleration is non-zero, while the center of mass acceleration remains zero if the disk does not translate. This indicates that additional forces must be acting on the disk, resulting in a net force of zero on the center of mass. Examples are provided to explore scenarios involving forces applied at the center of mass and opposing forces on the disk.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with concepts of linear and angular acceleration
  • Knowledge of uniform disk dynamics
  • Basic grasp of force vectors and equilibrium
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  • Explore the relationship between torque and angular acceleration in rigid body dynamics
  • Study the effects of applied forces on center of mass motion
  • Investigate examples of rotational motion in physics, focusing on uniform disks
  • Learn about the principles of static and dynamic equilibrium in mechanical systems
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Physics students, mechanical engineers, and anyone interested in the principles of rotational dynamics and force interactions in rigid bodies.

BadSkittles
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Hello, can someone explain to me what is the difference between center mass acceleration and angular acceleration? If i have an uniform disk laying still, then i give it a force to make it spin while it stays put. The angular acceleration obviously has a number. What about the acceleration of the center mass? Would this be zero since it is not moving?
 
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BadSkittles said:
Hello, can someone explain to me what is the difference between center mass acceleration and angular acceleration? If i have an uniform disk laying still, then i give it a force to make it spin while it stays put. The angular acceleration obviously has a number. What about the acceleration of the center mass? Would this be zero since it is not moving?

If the center of mass doesn't move (i.e., doesn't accelerate), it means that there must be at least one more force involved (besides the one that you give it yourself). This other force might be applied at the center of mass, or could be applied somewhere else on the disk, or could be the sum of one or more "other" forces. Whatever the case, if the center of mass of the disk does not accelerate, the vector sum of all forces involved add to zero.

I'll leave it to you to work out a couple of examples. What's the linear and angular accelerations if the "other" force is applied at the center of mass of the disk (for example, if the disk is on a stationary rotor shaft)? What is the linear and angular acceleration of the disk if the "other" force is an equal and opposite force on the opposite side of the disk?
 

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