First, we need to convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s) because the formula for torque requires the angular speed in rad/s.

1 revolution = 2π radians
1 minute = 60 seconds

So, 3600 rpm = 3600 * (2π / 60) = 377 rad/s

The moment of inertia (I) for a solid cylinder is given by the formula I = 0.5 * m * r^2, where m is the mass and r is the radius.

First, we need to convert the mass from pounds (lb) to kilograms (kg) because the formula for moment of inertia requires the mass in kg.

1 lb = 0.453592 kg

So, 3500 lb = 3500 * 0.453592 = 1587.57 kg

Next, we need to convert the diameter to radius and from inches to meters because the formula for moment of inertia requires the radius in meters.

1 inch = 0.0254 meters

So, 40 in. = 40 * 0.0254 = 1.016 m

The radius is half the diameter, so r = 1.016 / 2 = 0.508 m

Now we can calculate the moment of inertia:

I = 0.5 * 1587.57 kg * (0.508 m)^2 = 204.4 kg*m^2

The angular acceleration (α) can be calculated by dividing the change in angular speed by the time it takes for the change to occur.

α = (377 rad/s - 0 rad/s) / 10 s = 37.7 rad/s^2

Finally, we can calculate the torque (τ) using the formula τ = I * α:

τ = 204.4 kg*m^2 * 37.7 rad/s^2 = 7703.88 N*m

So, the torque required is approximately 7704 N*m.

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