Question

A particle moves in circle of radius 50m with a linear speed of 10m/s. The angular of velocity of the spatial is?

Answer 1

QuEstion:—

• A particle moves in circle of radius 50m with a linear speed of 10m/s. The angular of velocity of the particle is?

AnswEr:—

• The angular velocity of particle is 0.2 rad/s.

SteP By SteP ExplainaTion:—

• ${\mathfrak{Given}}\begin{cases}\sf{radius(r)=50\:m}\\ \ \sf{linear\:speed(v)=10ms^{-1}}\\ \ \sf{angular\: velocity(\omega)=?}\end{cases}$

$\underline{\mathfrak{To\:Find:}}$

angular speed

As we know that linear velocity =

$\sf{v=\omega r}\\ \\ \\ \longrightarrow \sf{\omega=\frac{v}{r}}$

Now, putting the values;

$\longrightarrow\sf{\omega=\frac{10}{50}}\\ \\ \\ \longrightarrow\sf{\omega=\frac{1\cancel{0}}{5\cancel{0}}}\\ \\ \\ \longrightarrow\bf{\omega=0.2\:rads^{-1}}$

ConcePt:—

• Rate of change of angular displacement with time is known as Angular velocity.
• It is a vector quantity.
• Direction of angular velocity can be obtained from right hand rule.
• Rate of change of angular velocity is known as angular acceleration.