The body in the given below figure is pivoted at $O$ and two forces act on it as shown. If $r_1=1.30 \mathrm{m}$, $r_2=2.15 \mathrm{m}, F_1=4.20 \mathrm{N}, F_2=4.90 \mathrm{N},$ ${\text{θ}}_1=75.0°$ and ${\text{θ}}_2=60.0°$, what is the net torque about the pivot?

   

The body in the figure shown below is pivoted at $O$. Three forces act on it, 

$F_A=12 \mathrm{N}$ at the point $A, 8.0 \mathrm{m}$ from $O$,

$F_B=14 \mathrm{N}$ at the point $B, 4.0 \mathrm{m}$ from $O$ and

$F_C=23 \mathrm{N}$ at the point $C, 3.0 \mathrm{m}$ from $O$. 

What is the net torque about $O$?

In the figure shown below, block $1$ has mass $m_1=460 \mathrm{g}$, block $2$ has mass $m_2=500 \mathrm{g}$, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius $R=5.00 \mathrm{cm}$. When released from rest, block $2$ falls $75.0 \mathrm{cm}$ in $5.00 \mathrm{s}$ without the cord slipping on the pulley.

$\left(a\right)$ What is the magnitude of the acceleration of the blocks? What are

$\left(b\right)$ tension $T_2$ and 

$\left(c\right)$ tension $T_1$?
$\left(d\right)$ What is the magnitude of the pulley's angular acceleration?
$\left(e\right)$ What is its rotational inertia?

In the figure shown below a cylinder having a mass of $3.0 \mathrm{kg}$ can rotate about its central axis through point $O$. Forces are applied as shown:$F_1=6.0 \mathrm{N}, F_2=4.0 \mathrm{N}, F_3=2.0 \mathrm{N},$ $F_4=5.0 \mathrm{N}$. Also, $r=5.0 \mathrm{cm}$, and $R=12 \mathrm{cm}$. Find the

$\left(a\right)$ magnitude and

$\left(b\right)$ direction of the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)

In the figure shown below, a uniform disk that can rotate around its centre like a merry-go-round. The disk has a radius of $2.00 \mathrm{cm}$ and a mass of $20.0$ gram and is initially at rest. Starting at time $t=0$, two forces are to be applied tangentially to the rim as indicated so that at time $t=1.25 \mathrm{s}$, the disk has an angular velocity of $250 \mathrm{rad} {\mathrm{s}}^{-1}$ counter-clockwise. Force $F_1$ has a magnitude of $0.100 \mathrm{N}$. What is magnitude of $F_2$?