What is the initial acceleration of the rod's CM?

In summary, a uniform rod of length 1.4 m is released from rest at an angle of 23° above the horizontal. The magnitude of the initial acceleration of the rod's center of mass can be found by looking at the net force acting on the center of mass and is composed of two components: tangential acceleration, which is proportional to the angular acceleration, and centripetal acceleration, which depends on the speed of rotation. As long as the rod is rotating, the center of mass will have some centripetal acceleration.
  • #1
BuBbLeS01
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Homework Statement


A uniform rod of length 1.4 m is attached to a frictionless pivot at one end. It is released from rest from an angle θ = 23° above the horizontal. Find the magnitude of the initial acceleration of the rod's CM.


Homework Equations


At = alpha * r


The Attempt at a Solution


I am reviewing old homework problems for my test tomorrow so I just have a few questions...
What is CM?
Also is At known as initial acceleration not Ac?
 
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  • #2
CM stands for 'Centre of Mass' and since the rod is uniform one can work out the acceleration by looking at the net force acting on the rod's CM.
 
  • #3
So is tangential acceleration known as initial acceleration not centripetal acceleration?
 
  • #4
BuBbLeS01 said:
So is tangential acceleration known as initial acceleration not centripetal acceleration?
No, the tangential acceleration is orthogonal to the centripetal acceleration by definition.
 
  • #5
In general, the acceleration of the center of mass (or any other point on the object) will have two components: centripetal and tangential. But what does the centripetal component depend upon?
 
  • #6
centripetal depends on the forces acting on the object I think
 
  • #7
BuBbLeS01 said:
centripetal depends on the forces acting on the object I think
Well, sure. But what I was going for was that centripetal acceleration depends on the speed of rotation. And immediately after this rod is released from rest, what is its initial rotational speed?
 
  • #8
0 rad/s^2, I guess I am don't understand the difference between at and ac and when to use which one.
 
  • #9
The tangential acceleration (which is proportional to the angular acceleration) has to do with the rate at which the angular speed changes. If the rate of rotation is constant, the tangential acceleration is zero.

But as long as the rod is rotating, the center of mass will have some centripetal acceleration.
 

What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity, which is the velocity along its circular path.

How is tangential acceleration different from centripetal acceleration?

Tangential acceleration is the component of acceleration that is parallel to the object's velocity, while centripetal acceleration is the component that is perpendicular to the object's velocity and towards the center of the circular path.

What factors affect tangential acceleration?

Tangential acceleration is affected by the object's tangential velocity, the radius of its circular path, and any external forces acting on the object, such as friction or gravity.

How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula a = v^2 / r, where v is the tangential velocity and r is the radius of the circular path.

Why is tangential acceleration important in physics?

Tangential acceleration plays a crucial role in understanding circular motion and the forces acting on objects moving in a circular path. It is also important in many real-world applications such as satellite orbits, amusement park rides, and car racing.

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