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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 terms of t; (6)

(ii) the time to bring to rest from a speed of 70π rads s^-1 , when I is 120 kg m² and τ is 80 Nm. (4)

(b) Evaluate ∫₁⁴(2 + 3√x + 1/√x)dx (6)