Answer
given,
cooling fan revolution = 850 rev/min
fan turns before revolution = 1500 revolutions


θ = 1500 revolution
θ = 1500 x 2 x π
θ = 9424.78 rad
a) using equation of rotation
ω² = ω₀² + 2 α θ
ω = 0 because body comes to rest
0 = 89² + 2 x α x 9424.78
α = -0.42 rad/s²
b) time take for the fan to stop
ω = ω₀ + α t
0 = 89 - 0.42 t

t = 211.9 s
Answer: c. Generally, metals are ductile.
Explanation:
From the options given in the question, the correct statement is that"Generally, metals are ductile.
Ductility of a metal simply means that a metal can be plastically deform before it is then fractured. It implies that metals can be drawn to thin wires. The only exception we have in this case is mercury.
Answer:
A) 
B) 
C) 
Explanation:
Given:
- mass of flywheel,

- diameter of flywheel,

- rotational speed of flywheel,

- duration for which the power is off,

- no. of revolutions made during the power is off,

<u>Using equation of motion:</u>



Negative sign denotes deceleration.
A)
Now using the equation:


is the angular velocity of the flywheel when the power comes back.
B)
Here:

Now using the equation:


is the time after which the flywheel stops.
C)
Using the equation of motion:


revolutions are made before stopping.
Answer: 3 radians/meter.
Explanation:
The general sinusoidal function will be something like:
y = A*sin(k*x - ω*t) + C
Where:
A is the amplitude.
k is the wave number.
x is the spatial variable
ω is the angular frequency
t is the time variable.
C is the mid-value.
The rule that we can use to solve this problem, is that the argument of the sin( ) function must be in radians (or in degrees)
Then if x is in meters, the wave-number must be in radians/meters, so when these numbers multiply the "meters" part is canceled.
Then for the case of the function:
y(x,t) = 0.1 sin(3x + 10t)
Where x is in meters, the units of the wave number (the 3) must be in radians/meters. Then the angular wave number is 3 radians/meter.