Is the angular acceleration of this rod constant?

[Prabs3257]

Homework Statement

There is a rod in a horizontal plane hinged on one end with a force applied on the other end i want to why am i getting different values of angular accel from when i am writing the equation about the hinged point and from the com shouldnt the angular acceleration be constant throughout the body

Relevant Equations

Torque = i α

Please refer to the image

 

[kuruman]

Please show your work. We cannot help you unless you show exactly what you have done. Also, please provide the exact statement of the problem.

 

[Prabs3257]

Please show your work. We cannot help you unless you show exactly what you have done. Also, please provide the exact statement of the problem.

Sorry i thought it got attatched but i have added it now

 

[kuruman]

The rod is pivoted about its end. Therefore you should use the moment of inertia about the pivot not about the CM in (2). You would use the moment of inertia about the CM if the rod were pivot-free on the plane.

 

[Prabs3257]

The rod is pivoted about its end. Therefore you should use the moment of inertia about the pivot not about the CM in (2). You would use the moment of inertia about the CM if the rod were pivot-free on the plane.

But i can write the torque equation about any point right ?? Please forgive me if i am sounding dumb

 

[jbriggs444]

But i can write the torque equation about any point right ?? Please forgive me if i am sounding dumb

If you use the torque equation about a point other than the pivot, you need to account for any linear force exerted by the pivot. You have proven that there must be such a force.

Of course, this is why we normally choose a particular reference axis -- so that we can ignore a particular parameter of the problem. For instance, the motion of the center of mass of the object or the linear force exerted by the pivot at one end.

 

[Prabs3257]

If you use the torque equation about a point other than the pivot, you need to account for any linear force exerted by the pivot. You have proven that there must be such a force.

Of course, this is why we normally choose a particular reference axis -- so that we can ignore a particular parameter of the problem. For instance, the motion of the center of mass of the object or the linear force exerted by the pivot at one end.

ohh you mean the pseudo force right now i get it thanks.

 

[kuruman]

It's a real force.

 

[jbriggs444]

ohh you mean the pseudo force right now i get it thanks.

Actually, a real force. If you push forward on one end of a freely floating rod, the other end will move rearward. The pivot prevents that by exerting a real forward force.

 

[Prabs3257]

It's a real force.

Sorry i meant the hinge force

 

[jbriggs444]

If, instead of the hinge, you had a freely floating rod then one could try to account for its motion using a pivot point located along the line where the hinge would have been.

Since the near end of the rod is accelerating rearward, the reference point for this motion would be accelerating rearward. Which would mean using an accelerating coordinate system. In order to transform this acceleration away, one could adopt an inertial pseudo-force and pretend that it acts forward on the center of mass of the rod.

The torque resulting from this pseudo-force would need to be accounted for in an angular momentum balance.

In the center-of-mass frame, this pseudo-force would still exist, but it would not produce any torque. This is why one prefers using the center-of-mass reference in the case of a freely floating rod.

 

[kuruman]

Using the CM frame also has the advantage that when an off-center impulse is delivered to the free rod, one can separate the momentum conservation equations into linear momentum of the CM and angular momentum about the CM. When the rod is pivoted, linear momentum is not conserved but angular momentum about the pivot is.