Dynamics Coursework; Angular Velocity, Springs, Force

In summary, the problem involves a rotating disc with a constant angular velocity of 240rpm, and sliding blocks attached to springs with a stiffness of 400N/m. The initial position of each block is x=25mm with no force in the spring. The task is to determine the value of x for each spring and calculate the normal force exerted by the side of the slot on the block. The mass of the springs and friction between the blocks and slots are neglected. A diagram is attached for reference.
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DTskkaii
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Homework Statement


The flat circular disc rotates about a vertical axis through O with a constant angular velocity of 240rpm. Prior to rotation, each of the 0.5kg sliding blocks has the position x=25mm with no force in its attached spring. Each spring has a stiffness of 400N/m, Neglect any friction between the blocks and the slots, and neglect the mass of the springs.

(a) Determine the value of x for each spring
(b) Calculate the normal force N exerted by the side of the slot on the block

I have attached the diagram.

Homework Equations


Not yet completely sure. If someone knows of a resource towards rotational velocity, that would be helpful, but I will update this section as soon as I have identified appropriate equations.

The Attempt at a Solution


As per above, I will upload something as soon as I can get a solid attempt down. I'm honestly incredibly lost on this question, it just seems like there are so many aspects happening at once.
 
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  • #2
Upload: diagram.
 

Attachments

  • dyna3.jpg
    dyna3.jpg
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1. What are the basic concepts of angular velocity?

The basic concept of angular velocity is the measurement of how fast an object is rotating around a fixed point. It is expressed in units of radians per second (rad/s) or degrees per second (°/s). It is also a vector quantity, meaning it has both magnitude and direction.

2. How does a spring's stiffness affect its behavior?

A spring's stiffness, also known as its spring constant, determines how much force is needed to stretch or compress the spring by a certain amount. The higher the stiffness, the more force is required to change its length. This directly affects the spring's behavior in terms of how it responds to external forces and how much it can stretch or compress.

3. Can you explain the relationship between force and acceleration in dynamics?

In dynamics, Newton's second law states that the force applied to an object is directly proportional to its mass and acceleration. This means that the greater the force applied to an object, the greater its acceleration will be. Additionally, the direction of the force and acceleration will be the same.

4. How does angular velocity relate to linear velocity?

Angular velocity and linear velocity are connected through the radius of rotation. The linear velocity of an object is the product of its angular velocity and the distance from the center of rotation. This means that the farther an object is from the center of rotation, the faster its linear velocity will be for a given angular velocity.

5. What are some real-life applications of the concepts covered in dynamics coursework?

The concepts of angular velocity, springs, and force are used in many real-life applications, such as designing and analyzing mechanical systems, understanding the motion of objects in circular motion, and predicting the behavior of springs in various engineering designs. These concepts are also fundamental in fields like robotics, aerospace engineering, and physics research.

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