Can a single force acting on a rigid body be the cause of pure rotational motion of the body? Suppose a single force acts on a disc in space at rest at a place other than its COM would the disc show both translational and rotational motion?
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3 Answers
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It is always true that:
$$ F = \frac{dp}{dt} \tag{1} $$
and:
$$ \tau = \frac{dL}{dt} \tag{2} $$
where $F$ and $\tau$ are the (net) force and the torque, and $p$ and $L$ are the linear and angular momenta. So if you apply a force it must change the linear momentum in accordance with equation (1) i.e. you cannot have pure rotational motion.
answered Jan 13, 2022 at 17:02
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$\begingroup$ If single force act the end of stick in free space ,will stick rotate around CoM and CoM will translate in straight line? $\endgroup$– 22flowerCommented Oct 6, 2023 at 8:47
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$\begingroup$ So if crosswind hit airplane, he will turn into wind due to big tail surface, he rotate around axis that passes through his c.g.? $\endgroup$– 22flowerCommented Oct 6, 2023 at 10:58
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$\begingroup$ But what if single force at the end of stick act continuosly 90 degress to stick, will stick rotate around com and com will translate in straight line ?Or then we will get pure rotation around com? $\endgroup$– 22flowerCommented Oct 8, 2023 at 21:33
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Can a single force acting on a rigid body be the cause of pure rotational motion of the body?
Yes. Assume that the body starts with some linear momentum $\vec p$ but no rotational motion. And suppose that we apply a force $\vec F =-\vec p/t$ for a time $t$. Then the body will end with no translational motion and if $\vec F$ is applied off center then it will have some rotational motion.
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Can a single force acting on a rigid body be the cause of pure rotational motion of the body?
You can only produce pure rotation with a couple. A couple consists of two equal and opposite parallel forces.
A single force whose line of action is not through the center of mass will produce rotation plus translation.
A single force whose line of action is through the center of mass will produce pure translation.
See the figures below.
Hope this helps.
