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
Magnitude of acceleration = (change in speed) / (time for the change).
Change in speed = (27 - 0) = 27 m/s
Time for the change = 10 s
Magnitude of acceleration = (27 m/s) / (10 s) = 2.7 m/s² .
Answer:
The human body runs at a constant 37 ºC but the air around you at room temperature is about 20-25 ºC which means heat is constantly leaving your body to warm your surroundings and maintain thermal equilibrium. You don't lose much energy doing this however as air heats reasonably quickly
Explanation:
Answer:
1.87 s
Explanation:
d = distance traveled by the water wave = 64 m
t = time taken to travel the distance = 14 s
= speed of water wave
Speed of water wave is given as
= 4.6 m/s
= wavelength of the wave = 859 cm = 8.59 m
T = period of the wave
period of the wave is given as
T = 1.87 s
