Torque

If force $\overrightarrow{F}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ acts on a particle having position vector $2\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then, the torque about the origin will be:

A particle of mass M tied to a string of length L is rotating along a circular path with constant speed $\mathrm{\vartheta }$. The torque on the particle is

If net external torque, about a point, acting on the system is zero, then we can surely say

A force of $\left(7\hat{\mathrm{i}}+3\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right) \mathrm{N}$ acts on a particle whose position vector is $\left(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\right) \mathrm{m}$. Find the torque experienced by the particle about the origin in $\mathrm{N}-\mathrm{m}$.

In the diagram, $a=5 \mathrm{cm}, b=20 \mathrm{cm}.$ Force$10 \mathrm{N} \text{and} 9 \mathrm{N}$ are in tangential direction and$12 \mathrm{N}$ is at an angle of $30°$ to the tangent. If the moment of inertia of the wheel is $3200 \mathrm{kg} {\mathrm{m}}^2$, its angular acceleration will be:

Example of a class one lever

Which physical quantity is represented by the product of the moment of inertia and angular acceleration?

A disk having a thread tightly wound on it is being pulled upwards by the thread such that the disk starts moving upwards with an acceleration $g$. If angular acceleration is $\alpha$ and radius $R$, then the value of $R\alpha$ is

An example of class three lever is

Torque is generally measured in units of

The figure here shows a uniform rod of mass m and length $\mathcal{l}$ at rest, in a gravity free region. The rod is hinged at one of its ends. The rod is oriented along y - axis, in the position shown here.




Suppose that the rod is made of charged non - conducting material. The linear charge density on the rod varies with distance $x$ from the hinge as $\lambda ={\lambda }_0{x}^n,$ here ${\lambda }_0$ is a constant and n is real number. The rod is in rest position and now a uniform electric field $E_0\widehat{i}$ is suddenly switched on in the region for an instant. Value of n, for which there is no reaction at the hinge, is

A uniform rod AB of mass m and length $\mathrm{l}\mathrm{ }$ is at rest on a smooth horizontal surface. An impulse p is applied to the end B. The time taken by the rod to turn through a right angle is

A uniform rod of mass $m$, length $\mathcal{l}$ rests on a smooth horizontal surface. Rod is given a sharp horizontal impulse $p$ perpendicular to the rod at a distance $\frac{\mathcal{l}}{4}$ from the centre. The angular velocity of the rod will be

Which of the following is conserved when the torque acting on a system is zero ?

A cylinder is rolling over frictionless horizontal surface with velocity ${\mathrm{v}}_0$ as shown in figure. Coefficient of friction between wall and cylinder is $\mathrm{\mu }=\frac{1}{4}$ . If the collision between cylinder and wall is completely inelastic, then kinetic energy of cylinder after collision -

In figure (a), a metre stick, half of which is wood and the other half steel is pivoted at the wooden end at $\mathrm{O}$ and a force is applied to the steel end at a. In figure (b), the stick is pivoted at the steel end at $\mathrm{O}\mathrm{\prime }$ and the same force is applied at the wooden end at $\mathrm{a}\mathrm{\prime }$ . The angular acceleration

What torque will increase angular velocity of a solid disc of mass 16 kg and diameter 1 m from zero to 120 rpm in 8 s?

A force of 100 N is applied perpendicularly to the left edge of the rectangle as shown in figure. The torque (magnitude and direction) produced by this force with respect to an axis perpendicular to the plane of the rectangle at corner $A$ and with respect to a similar axis at corner $B$ are respectively

A stone of mass $m$ tied to a string of length $l$ is rotating along a circular path with constant speed $v$. The torque on the stone is

Four 2 kg masses are connected by $\frac{1}{4}$ m spokes to an axle. A force of 24 N acts on a lever 1/2 m long produce angular acceleration $\mathrm{\alpha }$. The magnitude of $\mathrm{\alpha }$ in rad ${\mathrm{s}}^{-2}$ is