Question

The particle moves in a radius of 0.5m with linear velocity of 2 m/s. Find its angular speed.
A. 2 rad/s
B. 4 rad/s
C. 6 rad/s
D. 8 rad/s

Answer 1

Bigger the radius of the circle, smaller the angular velocity. Linear velocity and radius are given to us. Linear velocity divided by radius gives us angular velocity. You should represent angular as follows
$\omega =\dfrac{v}{r}$

Complete answer:
We are given radius (r) =0.5m, linear velocity (v) = 2m/s
Let us denote the angular velocity to be $\omega$.
We know,
$\omega =\dfrac{v}{r}$
Let us substitute the values on the above equation
$\omega =\dfrac{2}{0.5}=4rad/s$.

Therefore the answer is option (b).

Additional Information:
A system of physical units based on the meter, kilogram, second, ampere, kelvin, candela, and mole is known as the S.I. unit.
S.I. the unit of velocity is m/s.
S.I. unit of distance (radius) is m.
S.I. unit of angular velocity is rad/s.
Angular velocity is defined as how fast an object rotates or revolves relative to another point which is how soon the angular position or orientation of an object changes with time. There are two types of angular velocity namely orbital angular velocity and spin angular velocity.

Note:
Students should focus on remembering the formula and the units of the required parameters. Simple questions like these may turn out as a mistake with lack of attention. Angular velocity is a pseudo vector, with its magnitude measuring the rate at which an object rotates or revolves, and its direction is perpendicular to the present plane of rotation or angular displacement in three dimensions. The orientation of angular velocity is determined by the right-hand rule.