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.

first, get the moment of inertia for a thin rod, rotating as described.

angular momentum= momentinertia*175*2pI*60 rad/sec

tangential speed= 175*2PI*60*radius

To find the blade's angular momentum, you need to multiply its moment of inertia by its angular velocity. The moment of inertia for a thin rod rotating about its center of mass is given by the formula:

I = (1/12) * m * L^2

Where:
- I is the moment of inertia
- m is the mass of the propeller blade
- L is the length of the propeller blade

Plugging in the given values:
m = 83.2 kg
L = 2.24 m

I = (1/12) * 83.2 kg * (2.24 m)^2
I ≈ 6.68 kg·m^2

Next, given the angular velocity, you can calculate the angular momentum (L) using the formula:

L = I * ω

Where:
- L is the angular momentum
- I is the moment of inertia
- ω is the angular velocity

Plugging in the values:
ω = 175 rpm

Notice that ω needs to be converted from rpm to radians per second. To do this, you multiply by 2π/60, since there are 2π radians in a revolution and 60 seconds in a minute:

ω = 175 rpm * (2π rad/rev) / (60 s/min)
ω ≈ 18.33 rad/s

L = 6.68 kg·m^2 * 18.33 rad/s
L ≈ 122.17 kg·m^2/s

Therefore, the blade's angular momentum is approximately 122.17 kg·m^2/s.

To find the tangential speed at the blade tip, you can use the formula:

v = r * ω

Where:
- v is the tangential speed
- r is the radius (half of the length of the propeller blade)
- ω is the angular velocity

Since the length is given, you can find the radius (r) by dividing the length by 2:

r = 2.24 m / 2
r = 1.12 m

Plugging in the values:
ω = 18.33 rad/s

v = 1.12 m * 18.33 rad/s
v ≈ 20.53 m/s

Therefore, the tangential speed at the blade tip is approximately 20.53 m/s.

To find the angular acceleration (α) and torque (τ) required to stop the blade in 12.0 s, you can use the equations of rotational motion.

The final angular velocity (ωf) when the blade stops is 0 rad/s. The initial angular velocity (ωi) is 18.33 rad/s. The time (t) is given as 12.0 s.

The angular acceleration (α) can be calculated using the formula:

α = (ωf - ωi) / t

Plugging in the values:
ωf = 0 rad/s
ωi = 18.33 rad/s
t = 12.0 s

α = (0 rad/s - 18.33 rad/s) / 12.0 s
α ≈ -1.53 rad/s^2

The negative sign indicates that the blade is decelerating.

The torque (τ) required to stop the blade can be calculated using the formula:

τ = I * α

Plugging in the values:
I = 6.68 kg·m^2
α = -1.53 rad/s^2

τ = 6.68 kg·m^2 * -1.53 rad/s^2
τ ≈ -10.22 N·m

Therefore, the angular acceleration required to stop the blade is approximately -1.53 rad/s^2, and the torque required is approximately -10.22 N·m.