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Q8. (a) The angular velocity, ω radians per second, of a flywheel under a constant braking torque, τ newton metres, is given by:

I = dω/dt + τ = 0 Where I is its moment of inertia.

The time in seconds that lapse since the brake is applied is t.

Given that at time t = 0, ω = ω₀ , determine EACH of the following for a flywheel:

(i) an expression for ω in term of t. (6)

(ii) the time to bring to rest from a speed of 60π rads s^-1when I is 110 kgm² and τ is 85 Nm. (4)

b) Evaluate ∫_0.2^1.0400/V^1.4 dV (6)