An 83.2-kg propeller blade measures 2.24m end to end. Model the blade as a thin rod rotating about its center of mass. It's initially turning at 175rpm. Find the blade's angular momentum, the tangential speed at the blade tip, and the angular acceleration and torque required to stop the blade in 12.0s.

C = pi*D = 3.14 * 2.24 = 7.04m = Circumference of circle formed by rotating blade.

V=175rev/min * 6.28rad/rev * (1/60min/s
= 18.32rad/s.

1. M = mV = 83.2 * 1.57 = 130.6 = Angular momentum.

2. V=175rev/min * 7.04m/rev * (1/60)min/s = 20.53m/s.

3. a = (Vf - Vo) / t,
a = (0 - 18.32) / 12 = -1.53rad/s^2.

To find the blade's angular momentum, tangential speed at the blade tip, angular acceleration, and torque required to stop the blade, we can use the following formulas:

1. Angular momentum (L) = moment of inertia (I) × angular velocity (ω)
2. Moment of inertia (I) = mass (m) × length (L)
3. Tangential speed (v) = radius (r) × angular velocity (ω)
4. Angular acceleration (α) = change in angular velocity (Δω) / time (t)
5. Torque (τ) = moment of inertia (I) × angular acceleration (α)

Now, let's calculate each of these:

1. Angular momentum (L):
The moment of inertia for a thin rod rotating about its center is given by:
I = (1/12) × M × L²
where M is the mass and L is the length.

Given:
Mass (M) = 83.2 kg
Length (L) = 2.24 m

Substituting the values:
I = (1/12) × 83.2 kg × (2.24 m)²

Calculate the moment of inertia (I).

2. Tangential speed (v):
The tangential speed at the blade tip is given by the formula:
v = r × ω
where r is the radius and ω is the angular velocity.

Given:
Angular velocity (ω) = 175 rpm

To find the radius, divide the length of the blade by 2:
r = L / 2

Substitute the values and convert the angular velocity to radians per second (since the formula requires it):
ω = (175 rpm) × (2π rad/min) / (60 s/min)

Calculate the tangential speed (v).

3. Angular acceleration (α):
The angular acceleration is the change in angular velocity divided by time:
α = Δω / t

Given:
Time (t) = 12.0 s
The blade needs to stop, so the angular velocity (ω) will become 0.

Calculate the angular acceleration (α).

4. Torque (τ):
The torque required to stop the blade can be calculated using the formula:
τ = I × α

Given:
Calculate the torque (τ).

Once you have completed these calculations, you will have the values for the blade's angular momentum, tangential speed at the blade tip, angular acceleration, and torque required to stop the blade.