Question

A wheel of mass 2 kg and radius 10 cm is rotating about its axis at an angular velocity of 2π rad/s. The force that must be applied tangentially to the wheel to stop it in 5 revolutions is

• A. 3π×10⁻² kg-m²/s
• B. 4π× 10⁻² kg-m²/s
• C. π× 10⁻² kg-m²/s
• D. 2π× 10⁻² kg-m²/s

Answer 1

Answer: (D)

2π× 10⁻² kg-m²/s

Answer 2

Moment of inertia of wheel about its axis,

I = $\frac{mR^{2}}{2}$ = $\frac{2 \times (0.1)^{2}}{2}$ = 0.01 kg-m²

Now angular displacement, ∆θ = 2πn = 2π×5 = 10 π rad

∴ Angular retardation required, α = $\frac{\omega^{2}}{2\Delta\theta} = \frac{(2\pi)^{2}}{2 \times 10\pi}$ = π/5 rad/s²

∴ Torque required τ = Iα ⇒ FR = Iα

∴ F = $\frac{I\alpha}{R}$ = $\frac{0.01}{0.10} \times \frac{\pi}{5}$ = 2π×10⁻² N

Hence (4) is correct choice