An automobile engine develops $100 \ kW$ when rotating at a speed of $1800 \ rev/min$. What torque does it deliver in $N-m$?

If there is a change of angular momentum from $1 \, J \cdot s$ to $4 \, J \cdot s$ in $4 \, s$, then the torque is

Find the ratio of linear acceleration $(a)$ to angular acceleration $(\alpha)$ of the center of mass $(COM)$ for the given diagram. Given: $m = 2 \, kg$,$r = 10 \, cm = 0.1 \, m$,and force $F = 20 \, N$ applied at the center.

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

$A$ constant torque of $1000 \; Nm$ turns a wheel of moment of inertia $200 \; kg \cdot m^2$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $3 \; s$ is

$A$ mass of $10 \ kg$ is attached to one end of a massless rod and rotated in a circle of radius $30 \ cm$ with an angular velocity of $10 \ rad/s$. If the body is brought to rest in $10 \ s$ by applying a brake,the magnitude of the torque applied will be ...... $N-m$.