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

In summary, center mass acceleration and angular acceleration are two different types of acceleration that can occur when a force is applied to an object. While angular acceleration refers to the change in rotational motion, center mass acceleration refers to the change in linear motion of the object's center of mass. If the center of mass does not move, it means that the vector sum of all forces involved is zero. This indicates that there must be at least one additional force acting on the object besides the one applied by the individual. Examples include a force applied at the center of mass or an equal and opposite force on the opposite side of the object.
  • #1
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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  • #2
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?
 

1. What is center mass acceleration?

Center mass acceleration, also known as center of mass acceleration, is the rate of change of an object's velocity when it is moving in a straight line and its mass is centered at a single point.

2. How is center mass acceleration calculated?

Center mass acceleration is calculated by dividing the net force acting on an object by its mass. The formula for center mass acceleration is a = F/m, where a is acceleration, F is force, and m is mass.

3. What is the difference between center mass acceleration and center of mass?

Center mass acceleration refers to the rate of change of an object's velocity, while center of mass refers to the point at which an object's mass is evenly distributed. Center of mass remains constant, while center mass acceleration can change depending on the forces acting on an object.

4. How does center mass acceleration affect an object's motion?

Center mass acceleration affects an object's motion by determining how quickly its velocity changes. If the center mass acceleration is zero, the object will continue moving at a constant velocity. If the center mass acceleration is non-zero, the object's velocity will change over time.

5. What are some real-world applications of center mass acceleration?

Center mass acceleration is an important concept in physics and has many real-world applications. It is used in designing roller coasters, analyzing car crashes, and understanding the motion of celestial bodies. It is also essential in sports, such as diving and gymnastics, where athletes must control their center mass acceleration to perform complex movements.

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