The linear velocity of a rotating body is given by $\overrightarrow v = \overrightarrow \omega \times \overrightarrow r ,$where $\overrightarrow \omega $ is the angular velocity and $\overrightarrow r $ is the radius vector. The angular velocity of a body is $\overrightarrow \omega = \hat i - 2\hat j + 2\hat k$ and the radius vector $\overrightarrow r = 4\hat j - 3\hat k,$ then $|\overrightarrow v |$ is

Can you associate vectors with $(a)$ the length of a wire bent into a loop, $(b)$ a plane area, $(c)$ a sphere ? Explain.

A particle starting from rest, moves in a circle of radius $r$. It attains a velocity of $\mathrm{V}_{0} \;\mathrm{m} / \mathrm{s}$ in the $\mathrm{n}^{\text {th }}$ round. Its angular acceleration will be

A stone tied to $180 cm$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{ x }\,ms ^{-2}$. The value of $x.........\left(\text { Take } \pi=\frac{22}{7}\right)$

If the body is moving in a circle of radius $ r$ with a constant speed $v$, its angular velocity is

The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should