Determine the Maximum angular velocity

In summary, the problem involves a 10-lb rod attached to a 6-lb disk that rotates about a pivot. A spring of constant k = 4.5lb/ft is also attached to the disk. The assembly is released from rest and we are asked to calculate and plot the angular velocity of the assembly after it has rotated through an angle θ, and determine the maximum angular velocity and corresponding values of θ. To solve this, we can start with a free-body diagram and use torques to find the total torque on the assembly. This can then be plugged into the equation \tau = I \ddot\theta to get a differential equation for the angle. The work done in circular motion may also be
  • #1
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Homework Statement



The 10-lb slender rod AB is welded to the 6-lb uniform disk, which rotates about a pivot at A. A spring of constant k = 4.5lb/ft is attached to the disk and is unstretched when rod AB is horizontal. The assembly is released from rest in the position shown. Calculate and plot the angular velocity of the assembly after it has rotated through an angle θ, for values of θ from 0 to θm, the angle of maximum rotation. Determine the maximum angular velocity of the assembly and the corresponding values of θ.


http://image.cramster.com/answer-board/image/2009510199546337757939460712507371.jpg

Any help as to how to go about solving this would be greatly appreciated. I don't need it solved for me but info on how to set up the problem again would be appreciated. Thanks!

Homework Equations





The Attempt at a Solution

 
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  • #2
I'd start with a free-body diagram, but instead of forces, display torques about the fixed point at the center of the disk. Then add up all the torques to find the total torque on the assembly, and plug into [tex]\tau = I \ddot\theta[/tex] to get a differential equation for the angle.
 
  • #3
Hey pleasez
help me

Is the work done min circular motion zero?

next question:
What is the displacement of the blade of a fan when it worksss?
 

What is maximum angular velocity?

Maximum angular velocity is the highest possible speed at which an object can rotate around its axis. It is usually measured in radians per second (rad/s) or revolutions per minute (RPM).

How is maximum angular velocity calculated?

Maximum angular velocity can be calculated by dividing the angular displacement (change in angle) by the time it takes to make that change. This can be represented by the formula: ω = Δθ/Δt, where ω is the angular velocity, Δθ is the angular displacement, and Δt is the time.

What factors affect maximum angular velocity?

The maximum angular velocity of an object can be affected by its moment of inertia, which is a measure of its resistance to rotational motion. Other factors that can affect maximum angular velocity include the force applied and the shape and size of the object.

Why is maximum angular velocity important?

Maximum angular velocity is important because it helps scientists and engineers understand the rotational motion of objects. It is also a key factor in designing and optimizing machines and structures that involve rotational motion, such as engines and turbines.

What is the difference between maximum angular velocity and angular speed?

Maximum angular velocity refers to the highest possible speed at which an object can rotate, while angular speed is the rate of change of the angular displacement over time. Maximum angular velocity is a specific value, while angular speed can vary depending on the object's motion.

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