Question

When a particle is accelerated with a linear acceleration with 5 meter per second square and moves in a circular path of radius 2m then find the value of linear acceleration? ​

Answer 1

Ans: 2.5 rad/s^2

Exp:

let's take the formula of linear acceleration.

a = dv/dt

we know that v=r ω

where r is the radius and ω is the angular velocity

so we will substitute it in the formula

a=d(rω)/dt

=> a=r dω/dt

we know that dω / dt is the angular acceleration represented by α

a = r α (Remember this relation)

a is linear acceleration, α is angular acceleration.

substitute the values from the question.

5m/s^2 = 2m ( α )

α 5/2

α = 2.5 rad/ s^2 .

Answer 2

Correct Question:

When a particle is accelerated with a linear acceleration with 5 meter per second square and moves in a circular path of radius 2m then find the value of angular acceleration?

Solution:

• We know that angular acceleration is an axial vector directed perpendicular to the direction of linear acceleration.

• Let angular acceleration be $\alpha$ and linear acceleration be 'a'.

$\therefore \: \alpha = \dfrac{a}{r}$

$\implies \: \alpha = \dfrac{5}{2}$

$\implies \: \alpha = 2.5 \: rad/ {s}^{2}$

So, angular acceleration of particle is 2.5 rad/s².