Angular velocity, linear acceleration?

In summary, a rod of uniform density and thickness, with mass M and length L, is pivoted at one end and held at an angle θ below the horizontal. When released with no initial angular velocity, the rod experiences a linear acceleration of a at its free end. This can be found by using torque to determine the angular acceleration and then using that to calculate the linear acceleration. The necessary equations can be found in a textbook and the individual must gather them and attempt the problem themselves.
  • #1
silentshimmer
3
0
A rod of mass M, length L, and uniform density and thickness swings around a frictionless pivot at one end of the rod; the other end is free. The rod is held at angle θ below the horizontal and then released with no initial angular velocity, ω0=0. Find the linear acceleration a of the rod's free end immediately after the rod is released.
 
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  • #2
silentshimmer said:
A rod of mass M, length L, and uniform density and thickness swings around a frictionless pivot at one end of the rod; the other end is free. The rod is held at angle θ below the horizontal and then released with no initial angular velocity, ω0=0. Find the linear acceleration a of the rod's free end immediately after the rod is released.

Use torque to find the angular acceleration (gravity will act at the center of gravity of the object). Then use that to find the linear acceleration at the extremity.
 
  • #3
what equations do i need?
 
  • #4
silentshimmer said:
what equations do i need?

Well, you should look them up in your textbook. We can help people with assignments but they have to do most of the work and the first thing is to gather the necessary equations and take a stab at the problem.
 

1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates or revolves around a fixed axis. It is typically measured in radians per second or degrees per second.

2. How is angular velocity different from linear velocity?

Angular velocity measures the rotational speed of an object, while linear velocity measures the speed of an object in a straight line. Angular velocity takes into account the distance from the axis of rotation, while linear velocity does not.

3. What factors affect angular velocity?

Angular velocity is affected by the angular displacement, or how far the object has rotated, and the time it takes to rotate. It is also influenced by the moment of inertia, or the object's resistance to rotational motion, and any external forces acting on the object.

4. How is angular velocity related to linear speed?

Angular velocity and linear speed are related through the radius of rotation. The linear speed of a point on a rotating object is equal to the angular velocity multiplied by the radius of rotation.

5. Can angular velocity change over time?

Yes, angular velocity can change over time if the rotational speed of the object changes or if the axis of rotation shifts. The change in angular velocity is known as angular acceleration, which is measured in radians per second squared or degrees per second squared.

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