Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 3: Exercise-3

A turning moment of $100 \mathrm{Nm}$ is applied to a shaft which passes through a wheel of radius $R=50\mathrm{cm}.$ The force with which brakes must be applied to the wheel (see figure) so that the wheel does not rotate is...... $\times {10}^2 N.$ The coefficient of friction equals $0.25.$

A cylinder of mass $5 \mathrm{kg}$ and radius $30 \mathrm{cm},$ and free to rotate about its axis, receives an angular impulse of $3 \mathrm{kg}{ \mathrm{m}}^2{ \mathrm{s}}^{-1}$ initially followed by a similar impulse after every $4 \mathrm{s}.$ What is the angular speed (in rad/sec) of the cylinder after $30 \mathrm{s}$ of the initial impulse(write the value to the nearest integer)? The cylinder is at rest initially.

A uniform rod of mass $8m$ and length $6a$ is lying on a horizontal table. Two point masses $m$ and $2m$ moving with speed $2v$ and $v$ respectively strike the rod and stick to it as shown in the figure. Kinetic energy of the system after collision is given by $\alpha \times m{v}^2.$ The value of $\alpha$ is

A stick of length $L$ and mass $M$ lies on a frictionless horizontal surface on which it is free to move in anyway. A ball of mass $m$ moving with speed $v$ as shown in fig. Mass of the ball so that it remains at rest immediately after collision is $\frac{M{L}^2}{\left({ L}^2+K{d}^2\right)}.$ The value of $K$ is.

A rod of length $l$ and mass $M$ held vertically is let go down, without slipping at the point of contact. Velocity of the top end at the time of touching the ground is $v.$ Find the value of $\frac{v^2}{gl}$

A light rod carries three equal masses $A, B$ and $C$ as shown in figure. Velocity of $B$ in vertical position of rod, if it is released from horizontal position as shown in figure is $V\mathit{.}$ Value of $7\frac{{ V}^2}{gl}.$

An initial momentum is imparted to a homogeneous cylinder as a result of which it begins to roll without slipping up an inclined plane at speed $v_0=4{ ms}^{-1}.$ The plane makes an angle of $30°$ with the horizontal. What time (in sec) does the cylinder take before stopping.

As shown in the figure, a rod moves with $v=2 \mathrm{m} {\mathrm{s}}^{-1}$ and rotates with $\omega =2\pi \mathrm{rad} {\mathrm{s}}^{-1}$. The point on the rod whose velocity is zero in this frame is at a distance $\frac{\beta }{\pi } \mathrm{m}$ below the centre of mass. Write the value of $\beta$.