Question

find the angular acceleration of a particle in circular motion , which slows down from 300r.m.p to 0 r.p.m in 20 seconds.​

Answer 1

Given:

initial frequency n₁ = 300 r.p.m

final frequency n₂ = 0 r.p.m

To find:

angular acceleration α =?

Step-by-step explanation:

• In a circular motion, the angular speed slows down from 300r.m.p to 0 r.p.m in 20 seconds.​
• So first we have to convert the angular speed given in r.p.m to r.p.s.
• To convert  r.p.m to r.p.s. divide r.p.m speed by 60.

       n₁ = $\displaystyle \frac{300}{60}$ = 5 r.p.s.

       n₂ = $\displaystyle \frac{0}{60\\}$ = 0

• The angular acceleration is given by:

$\displaystyle \alpha = \frac{\omega_2-\omega_1}{t} = \frac{2\pi n_2-2\pi n_1}{t}$

where

α = angular acceleration

ω₂ = final angular speed

ω₁ = initial angular speed

t = time

n₁ = initial frequency

n₂ = final frequency

• Put given values in the above equation to find the angular acceleration.

       $\displaystyle \alpha =\frac{2\pi (0)-2\pi (5)}{20}$

       α = - 1.57 rad/s²

• The negative sign shows that the angular acceleration of a particle in circular motion is decreased.

         α = 1.57 rad/s²

• Hence, the required angular acceleration is 1.57 rad/s².