Write the formula of work done by torque in rotational rigid body about a the fixed axis.
A disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$, is .....
A flywheel has moment of inertia $4\ kg - {m^2}$ and has kinetic energy of $200\ J$. Calculate the number of revolutions it makes before coming to rest if a constant opposing couple of $5\ N - m$ is applied to the flywheel .......... $rev$
A $70\, kg$ man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force $F$ to raise himself The center of gravity rises by $0.5\, m$ before he leaps. After the leap the $c.g.$ rises by another $1\, m$. The maximum power delivered by the muscles is : (Take $g\, = 10\, ms^{-2}$)
A thin hollow cylinder open at both ends:
$(i)$ Slides without rotating
$(ii)$ Rolls without slipping, with the same speed
One end of a straight uniform $1\; \mathrm{m}$ long bar is pivoted on horizontal table. It is released from rest when it makes an angle $30^{\circ}$ from the horizontal (see figure). Its angular speed when it hits the table is given as $\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},$ where $\mathrm{n}$ is an integer. The value of $n$ is