The circular blade on a radial arm saw is turning at 293 rad/s at the instant the motor is turned off. In 17.9 s, the speed of the blade is reduced to 60 rad/s. Assume the blade to be a uniform solid disk of radius 0.17 m and mass 0.400 kg. Find the magnitude of the net torque applied to the blade.

To find the net torque applied to the blade, we need to use the rotational motion equation involving torque and moment of inertia. The moment of inertia for a uniform solid disk about its axis of rotation is given by the equation:

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

where I is the moment of inertia, m is the mass, and r is the radius of the disk.

Given:
Mass of the disk, m = 0.400 kg
Radius of the disk, r = 0.17 m

We can calculate the moment of inertia for the disk using the given values:

I = (1/2) * 0.400 kg * (0.17 m)^2

Next, let's calculate the initial angular velocity of the blade using the given information:

Initial angular velocity, ω_i = 293 rad/s

The final angular velocity of the blade is given as:

Final angular velocity, ω_f = 60 rad/s

The change in angular velocity can be calculated as:

Δω = ω_f - ω_i

Now, we need to calculate the time taken for the change in angular velocity using the equation:

Δω = α * t

where α represents the angular acceleration, and t is the time taken.

Since the blade is slowing down, the angular acceleration can be calculated as:

α = (Δω) / t

Given:
Time, t = 17.9 s

Next, calculate the angular acceleration:

α = (60 rad/s - 293 rad/s) / 17.9 s

Now that we have the moment of inertia (I) and the angular acceleration (α), we can calculate the net torque (τ) using the equation:

τ = I * α

Finally, substitute the values into the equation to find the magnitude of the net torque applied to the blade.