Question

A body moves along a circular path of radius $10\,m$ and the coefficient of friction is $0.5.$ What should be its angular velocity in rad/s if it is not to slip from the surface?(Take $g = 10\,m{s^{ - 2}}$)

Answer 1

Let us first talk about Circular motion. In a circular direction, motion is defined as the change in location of an object with respect to its surroundings. Circular Motion is when an object moves around the circumference of a globe. We call it "Uniform Circular Motion" when a body travels in a circular direction at a constant speed.

Complete step by step answer:
Angular velocity, also known as angular frequency vector, is a vector measure of rotation rate in physics that refers to how quickly an object rotates or spins relative to another point, i.e. how quickly the angular position or orientation of an object changes with time.

Angular velocity can be divided into two categories. The rate at which a point object orbits around a fixed origin, or the time rate at which its angular location changes relative to the origin, is referred to as orbital angular velocity. In comparison to orbital angular velocity, spin angular velocity refers to how rapidly a rigid body rotates with respect to its centre of rotation and is independent of the choice of origin.

Given: Radius $= 10m$, Coefficient of friction ($\mu$)$= 0.5$
The velocity must be calculated, using the velocity formula:
$v = \sqrt {\mu \times r \times g} = \sqrt {0.5 \times 10 \times 10} \\\ \Rightarrow v = 7.07\,m/s$
The angular velocity must be calculated, using the angular velocity formula:
$v = r\omega \\\ \Rightarrow \omega = \dfrac{v}{r} \\\ \Rightarrow \omega= \dfrac{{7.07}}{{10}} \\\ \therefore \omega = 0.707\,rad/s$

Hence, the angular velocity is 0.707 rad/s.

Note: In general, angular velocity has an angle per unit time dimension (angle replacing distance from linear velocity with time in common). The SI unit of angular velocity is radians per second, and since the radian is a dimensionless number, the SI units of angular velocity may be listed as ${s^{ - 1}}$.