# In pure translation why the body does not exhibit rotation only and only about the CM? [closed] Suppose I have a rod in pure translation as shown in the picture with some constant acceleration. The two forces $F_1$ and $F_2$ act as shown. So clearly due to the definition of pure translation every point in the rod has the same velocity (say $\vec v$) so relative velocity of any point w.r.t to another point on the rod must be zero.

But, if I consider the net torque about $A$(or $O$), clearly, there is a non-zero torque due to $F_2$ ( or $F_1$ if you consider $O$) so clearly there must be some angular acceleration about that point. which would mean that the there is some non-zero relative velocity of other points on the rod about $A$(or $O$)

I don't understand what I'm getting wrong here.

And from what I read the rod must have no rotational motion only and only about the Centre of Mass. why is so ?

Please please explain to me clearly.

## closed as unclear what you're asking by ja72, ACuriousMind♦, user36790, CuriousOne, GertJun 15 '16 at 1:30

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• When an object experiences pure translational motion, all of its points move with the same velocity as the center of mass; that is in the same direction and with the same speed-i wonder how those two forces appear in your problem? – drvrm Mar 12 '16 at 12:55
• Check Irodov's Problems in General Physics. The first one i think in dynamics of a rigid body. you'll know – Subhranil Sinha Mar 12 '16 at 14:16
• I realized I understood your question in a different way so don't mind my answer. For a more spot-on answer, you can look at this : physics.stackexchange.com/questions/93698/… – Starior Mar 12 '16 at 16:08
• You have specified the forces applied and the acceleration state. Unfortunately they are inconsistent as specified. – ja72 Jun 8 '16 at 14:10
• Possible duplicate of Do objects rotate around the torque vector or its center? – ja72 Jun 8 '16 at 14:10

## 1 Answer

In this case, the rod cannot experience only pure translation. Because resultant torque acting on the rod isn’t equal to zero.

If acting points of the forces are fixed, the rod will rotate counter clockwise until it is parallel with the forces. So, until that final state of the rod is established (without damping forces, this state will never be established), the rod will experience both of rotational and translational motions.

• Without damping forces the oscillations would continue indefinitely – Rick Jun 7 '16 at 17:56
• I think the oscillations will be removed finally even without damping forces. – lucas Jun 7 '16 at 18:08
• They would not... the torque about the COM would be exactly proportional to the sine of the angle from horizontal. The corresponding differential equation would then be: $\ddot \theta = k sin(\theta)$ which is equivalent to an ideal (undamped) pendulum which will oscillate forever. – Rick Jun 7 '16 at 18:24