To find the angular velocity of the flywheel at the end of the 5-second period, we can use the formula:

Torque = Moment of Inertia * Angular Acceleration

The moment of inertia (I) of a flywheel is given by the formula:

I = (1/2) * m * r^2

where m is the mass of the flywheel and r is its radius.

Plugging in the given values:

I = (1/2) * 10 kg * (0.2 m)^2
= (1/2) * 10 kg * 0.04 m^2
= 0.2 kg * m^2

Now, we can rearrange the formula for torque to solve for angular acceleration:

Angular Acceleration = Torque / Moment of Inertia

Plugging in the given torque of 50 N·m:

Angular Acceleration = 50 N·m / 0.2 kg·m^2
= 250 rad/s^2

Finally, we can find the angular velocity (ω) at the end of the 5-second period using the formula:

Angular Velocity = Initial Angular Velocity + (Angular Acceleration * Time)

Since the flywheel is initially at rest, the initial angular velocity is 0 rad/s. Plugging in the values:

Angular Velocity = 0 rad/s + (250 rad/s^2 * 5 s)
= 0 rad/s + 1250 rad/s
= 1250 rad/s

Therefore, the angular velocity of the flywheel at the end of the 5-second period is 1250 rad/s.

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