Question

A wheel of moment of inertia 2 kg m² is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad/s. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is ______. 

Options

• 24 kg m²/s

• 48 kg m²/s

• 72 kg m²/s

• 96 kg m²/s

Answer 1

A wheel of moment of inertia 2 kg m² is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad/s. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is 72 kg m²/s. 

Explanation:

According to question, I = 2kg m²

ω₀ = 60 rad/s, ω = 0

t = 5 min = 5 × 60 = 300s

using, ω = ω₀ + αt ⇒ α = `(omega-omega_0)/"t"`

= `(0-60)/300=(-60)/300=(-1)/5`rad/s²

For t = 2 min

 ω = ω₀ + αt

= `60-1/5xx120` = 60 - 24 ⇒ ω = 36 rad/s

Angular momentum,

L = 1ω = 2 × 36 = 72 kg m²/s