Answer:
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Explanation:
We can simulate this system as a physical pendulum, which is a pendulum with a distributed mass, in this case the angular velocity is
w² = mg d / I
In this case, the distance d to the pivot point of half the length (L) of the cylinder, which we consider long and narrow
d = L / 2
The moment of inertia of a cylinder with respect to an axis at the end we can use the parallel axes theorem, it is approximately equal to that of a long bar plus the moment of inertia of the center of mass of the cylinder, this is tabulated
I = ¼ m r2 + ⅓ m L2
I = m (¼ r2 + ⅓ L2)
now let's use the concept of density to calculate the mass of the system
ρ = m / V
m = ρ V
the volume of a cylinder is
V = π r² L
m = ρ π r² L
let's substitute
w² = m g (L / 2) / m (¼ r² + ⅓ L²)
w² = g L / (½ r² + 2/3 L²)
L >> r
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Answer:
any object that has density more than 1.4
Explanation:
The object that has density more than 1.4 is denser than the honey
Answer:
f1= -350cm or -3.5m
f2= 22.1cm or 0.221m
Explanation:
A person is nearsighted when the person's far point is less than infinity. A diverging lens is normally used to correct this eye defect. A diverging lens has a negative focal length as seen in the solution attached.
Farsightedness is when a person's near point is farther than 25cm. This eye defect is corrected using a converging lens. The focal length of a converging lens is positive. This is evident in the solution attached. The near point is also referred to as the least distance of distinct vision.
Before the launch, the momentum of the (spacecraft + asteroid) was zero. So after the launch, the momentum of the (spacecraft + asteroid) has to be zero.
Momentum = (mass) x (velocity)
Momentum after the launch:
Spacecraft: (1,000 kg) x (250 m/s) = 250,000 kg-m/s
Asteroid: (mass) x (-25 m/s)
Their sum: 250,000 - 25(mass) .
Their sum must be zero, so 250,000 kg-m/s = (25 m/s) x (mass)
Divide each side by 25 : 10,000 kg-m/s = (1 m/s) x (mass)
Divide each side by (1 m/s) : 10,000 kg = mass
