Question

A fly wheel, rotating with an angular velocity of 88 rad/s, slows down at a constant rate of 2 rad/s^2.

Find the time

required by it to stop rotating.​

Answer 1

Given :

Initial angular velocity = 88 rad/s

Final angular velocity = zero

Angular acceleration = 2 rad/s²

To Find :

Time taken by fly wheel to stop rotating.

Solution :

❖ Angular acceleration is defined as the rate of change of angular velocity.

• It is an axial vector quantity$.$
• It has both magnitude as well as direction.
• SI : rad/s²

Formula : α = ω₂ - ω₁ / t

» α denotes angular acceleration

» ω₂ denotes final angular velocity

» ω₁ denotes initial angular velocity

» t denotes time

By substituting the given values;

➙ α = ω₂ - ω₁ / t

➙ -2 = 0 - 88 / t

[Negative sign of angular acceleration shows that angular velocity decreases with time.]

➙ t = -88/(-2)

➙ t = 44 s

Answer 2

Given :

Initial angular velocity = 88 rad/s

Final angular velocity = zero

Angular acceleration = 2 rad/s²

To Find :

Time taken by fly wheel to stop rotating.

Solution :

❖ Angular acceleration is defined as the rate of change of angular velocity.

It is an axial vector quantity$.$

It has both magnitude as well as direction.

SI : rad/s²

Formula : α = ω₂ - ω₁ / t

» α denotes angular acceleration

» ω₂ denotes final angular velocity

» ω₁ denotes initial angular velocity

» t denotes time

By substituting the given values;

➙ α = ω₂ - ω₁ / t

➙ -2 = 0 - 88 / t

[Negative sign of angular acceleration shows that angular velocity decreases with time.]

➙ t = -88/(-2)

➙ t = 44 s