Question

Consider a rotating object that is accelerated from rest to 20000 remote in 5 minutes. What is the angular acceleration?

Answer 1

$\checkmark$ Given:

Consider a rotating object that is accelerated from rest to 20000 rpm

(rotation per minute) in 5 minutes

$\checkmark$ To Find:

The angular acceleration

$\checkmark$ Solution:

We know that,

$\red{\bigstar \ \boxed{\rm \alpha=\dfrac{\Delta \omega}{\Delta t}}}$

Here,

• α = angular acceleration
• Δω = change in angular velocity
• Δt = change in time

According to the Question,

We are asked to find the angular acceleration

So, we must find "α"

Given that,

Consider a rotating object that is accelerated from rest to 20000 rpm

(rotation per minute) in 5 minutes

Hence,

→ ω = 20000 rpm

Converting rpm to rad/s

[1 rpm = 0.10472 rad/s]

Hence,

$\star$ ω = 2100 rad/s

and,

→ t = 5 minutes

Converting minutes to seconds

[1 minute = 60 seconds]

Hence,

$\star$ t = 300 seconds

Here,

• Δω = 2100 rad/s
• Δt = 300 seconds

By Substituting the values,

We get,

$\blue{\rm \implies \alpha=\dfrac{2100}{300} \ rad/s^{2}}$

On further simplification,

We get,

$\pink{\rm \implies \alpha=7 \ rad/s^{2}}$

Therefore,

Angular Acceleration (α) = 7 rad/s²