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The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?
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Verified Answer
The correct answers are:
The forces may be acting radially from a point on the axis
,
The forces may be acting on the axis of rotation
,
The forces may be acting parallel to the axis of rotation
,
The torque caused by some forces may be equal and opposite to that caused by other forces
The forces may be acting radially from a point on the axis
,
The forces may be acting on the axis of rotation
,
The forces may be acting parallel to the axis of rotation
,
The torque caused by some forces may be equal and opposite to that caused by other forces
The torque on a system of particles
$$
\vec{\tau}=\vec{r} \times \vec{F}=r F \sin \theta \hat{n}
$$
where, $\theta$ is angle between $\vec{r}$ and $\vec{F}$, and $\hat{n}$ is a unit vector perpendicular to the plane of both $\vec{r}$ and $\vec{F}$.
(a) If forces act radially in the direction $\vec{r}, \theta=0$ hence $\tau \mid=0 \quad$ [from Eq. (i)]
(b) If forces are acting on the axis of rotation, then $\theta=0^{\circ}$, $r=0,|\tau|=0$ [from Eq . (i)]
(c) If forces acting parallel to the axis of rotation then its component in plane of $\vec{r}$ and $\vec{F}$ is $F \cos 90^{\circ}=0$
[from Eq . (i)]
(d) If torque by forces are equal and opposite then net torque, $\tau_{\text {net }}=\tau_1-\tau_2=0$
$$
\vec{\tau}=\vec{r} \times \vec{F}=r F \sin \theta \hat{n}
$$
where, $\theta$ is angle between $\vec{r}$ and $\vec{F}$, and $\hat{n}$ is a unit vector perpendicular to the plane of both $\vec{r}$ and $\vec{F}$.
(a) If forces act radially in the direction $\vec{r}, \theta=0$ hence $\tau \mid=0 \quad$ [from Eq. (i)]
(b) If forces are acting on the axis of rotation, then $\theta=0^{\circ}$, $r=0,|\tau|=0$ [from Eq . (i)]
(c) If forces acting parallel to the axis of rotation then its component in plane of $\vec{r}$ and $\vec{F}$ is $F \cos 90^{\circ}=0$
[from Eq . (i)]
(d) If torque by forces are equal and opposite then net torque, $\tau_{\text {net }}=\tau_1-\tau_2=0$
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