Physics, 19.12.2019 05:31 zeesharpe05

Apropeller consists of two blades each 3.0 m in length and mass 120 kg each. the propeller can be approximated by a single rod rotating about its center of mass. the propeller starts from rest and rotates up to 1200 rpm in 30 seconds at a constant rate.

a) what is the angular momentum of the propeller at =10s; =20s?
b) what is the torque on the propeller?

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Answer from: Ashleymsmith

Explanation:

= length of each blade = 3 m

= mass of each blade = 120 kg

= length of the rod

= mass of the rod

Length of the rod is given as

L = 2 l = 2 (3) = 6 m

$w_{0}$ = Angular velocity at t = 0, = 0 rad/s

$w_{30}$ = Angular velocity at t = 30, = 1200 rpm = 125.66 rad/s

$\Delta t$ = time interval = 30 - 0 = 30 s

angular acceleration is given as

$\alpha = \frac{w_{30} - w_{0}}{\Delta t} = \frac{125.66 - 0}{30} = 4.2 rad/s^{2}$

Angular velocity at t = 10 s is given as

$w_{10} = w_{0} + \alpha t\\w_{10} = 0 + (4.2) (10)\\w_{10} = 42 rad/s$

Angular velocity at t = 20 s is given as

$w_{20} = w_{0} + \alpha t\\w_{20} = 0 + (4.2) (20)\\w_{10} = 84 rad/s$

Mass of the rod is given as

M = 2m = 2(120) = 240 kg

Moment of inertia of the propeller is given as

$I = \frac{ML^{2} }{12} = \frac{(240)(6)^{2} }{12} = 720 kgm^{2}$

Angular momentum at t = 10 s is given as

$L_{10} = I w_{10} = (720) (42) = 30240 kgm^{2}/s$

Angular momentum at t = 20 s is given as

$L_{20} = I w_{20} = (720) (84) = 60480 kgm^{2}/s$

Torque on propeller is given as

$\tau = I \alpha \\\tau = (720) (4.2)\\\tau = 3024 Nm$

Answer from: Quest

answer: good job it's all correct !

explanation:

Iwill mark as the brainliest answer check if the answers are correct

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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Apropeller consists of two blades each 3.0 m in length and mass 120 kg each. the propeller can be ap...

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