Kinematics of Rotational Motion about a Fixed Axis

A disc of moment of inertia $5 \mathrm{kg} {\mathrm{m}}^2$ is acted upon by a constant torque of $20 \mathrm{Nm}$. If the angular velocity changes from $30 \mathrm{rad}/\mathrm{s}$ to $50 \mathrm{rad}/\mathrm{s}$. The angle rotated by the wheel is

A disc of radius $R$ rolls on a rough horizontal surface. The distance covered by the point $A$ in one revolution is

The angular velocity of a particle is given by $\mathrm{\omega }=1.5\mathrm{t}-3{\mathrm{t}}^2+2$, $$ , Find the time when its angular acceleration $(\mathrm{in} \mathrm{rad}/{\sec }^2)$becomes zero. 

The angular speed of a motor wheel is increased from $1200\mathrm{rpm}$ to $3120\mathrm{rpm}$ in $16$ seconds. The angular acceleration of the motor wheel is

A particle is rotating m circle with speed $10\pi \mathrm{rad} {\mathrm{s}}^{-1}$ with acc $-2\pi \mathrm{rad} {\mathrm{s}}^{-2}$, then calculate:

(i) Time after which it comes to rest.

(ii) After how many rotations will it come to rest.

State the laws of motion for rotating bodies.

Can we use the equations of rotational motion if $\theta$ is measured in degrees and not in radian ?

A grindstone has moment of inertia $600 \mathrm{kg} {\mathrm{m}}^2$. A constant couple is applied on it. As a result it acquires a speed of $150 \mathrm{rpm}$ in $10 \mathrm{s}$, after starting from rest. Calculate the couple.

A flywheel has a mass $200 \mathrm{kg}$  and radius of gyration $0.6 \mathrm{m}$. It is given an angular speed of $150 \mathrm{rpm}$ in $90$  rotations starting from rest. Determine the torque assuming it to be constant that acted on the flywheel.

A uniform disc of moment of inertia $1 \mathrm{kg} {\mathrm{m}}^2$ rotates with a speed of $120 \mathrm{rpm}$. Calculate the torque required to stop the disc in $10$ revolutions?

A thin rod of the length $L$ is suspended from one end and rotates with $n$ rotation per second, the rotational kinetic energy of rod will be?

A uniform solid sphere of mass $m$ and radius $r$ is projected along a rough horizontal surface with the initial velocity $v_0$ and angular velocity ${\omega }_0$ as shown in the figure. If the sphere finally comes to complete rest, then $\frac{2{\omega }_{0}r}{v_0}$ is equal to

A wheel rotating with uniform angular acceleration covers $50$ rev in the first five seconds after the start. If the angular acceleration at the end of five seconds is $x\pi$ $\mathrm{rad} {\mathrm{s}}^{-2}$, find the value of $x$.

How do we relate quantities of rotational kinematics and translational kinematics?

A potter's wheel is rotating with a constant acceleration of $4.0 \mathrm{rad} {\mathrm{s}}^{-2}$. How many revolutions will it make in $5 \mathrm{seconds}$? The wheel was initially at rest.

A rigid body under pure rotation is uniformly accelerated.The tangential acceleration $a$ of a particle of the body, the distance $r$ of the particle from the axis, and the angular acceleration $\alpha$ of the body are related as $\alpha =\frac{a}{r}$. Thus:

Define constant angular velocity.

Starting from rest, a fan takes $4 \mathrm{s}$ to attain the maximum speed of $360$ revolutions per minute. Assuming constant acceleration, find the time taken by the fan in attaining half the maximum speed.

A uniform rod of length $l$ and mass $M$ is suspended from two inextensible string as shown in the figure. What will be the tension in the left string when right string snaps?

An object changes its rotational speed from $10 \mathrm{rad}/\mathrm{s}$ to $20 \mathrm{rad}/\mathrm{s}$ in $5 \mathrm{s}$. Find the angular acceleration of the object?