Answer:
75 rad/s
Explanation:
The angular acceleration is the time rate of change of angular velocity. It is given by the formula:
α(t) = d/dt[ω(t)]
Hence: ω(t) = ∫a(t) dt
Also, angular velocity is the time rate of change of displacement. It is given by:
ω(t) = d/dt[θ(t)]
θ(t) = ∫w(t) dt
θ(t) = ∫∫α(t) dtdt
Given that: α (t) = (6.0 rad/s4)t² = 6t² rad/s⁴. Hence:
θ(t) = ∫∫α(t) dtdt
θ(t) = ∫∫6t² dtdt =∫[∫6t² dt]dt
θ(t) = ∫[2t³]dt = t⁴/2 rad
θ(t) = t⁴/2 rad
At θ(t) = 10 rev = (10 * 2π) rad = 20π rad, we can find t:
20π = t⁴/2
40π = t⁴
t = ⁴√40π
t = 3.348 s
ω(t) = ∫α(t) dt = ∫6t² dt = 2t³
ω(t) = 2t³
ω(3.348) = 2(3.348)³ = 75 rad/s
The isobars in the conventional series that will be needed
to complete the pressure analysis between the lowest and highest values on this
map are: 1008, 1012, 1016, 1020.
To add, an isobar is <span>a line on a map connecting points having the
same atmospheric pressure at a given time or on average over a given period.</span>
There are 3 significant figures, if that answers the question.
Explanation:
Displacement = 5 km
A.
Converting km/h to m/s,
10 km/h * 1000 m/1 km * 1 h/3600 s
= 25/9 m/s
Remember,
700 watt = 700 J/s
Velocity = displacement/time
Time = 5000/(25/9)
= 1800 s
Energy = power * time
= 700 * 1800
= 1,260,000
= 1260 kJ
B.
Converting km/h to m/s,
3 km/h * 1000 m/1 km * 1 h/3600 s
= 5/6 m/s
290 watt = 290 J/s
Velocity = displacement/time
Time = 5000/(5/6)
= 6000 s
Energy = power * time
= 290 * 6000
= 1,740,000
= 1740 kJ
C.
Walking burns more energy; 1,740,000 joules. It burns more because you walk for a greater period of time.
Answer:
w=3.05 rad/s or 29.88rpm
Explanation:
k = coefficient of friction = 0.3900
R = radius of the cylinder = 2.7m
V = linear speed of rotation of the cylinder
w = angular speed = V/R or to rewrite V = w*R
N = normal force to cylinder
N=


These must be balanced (the net force on the people will be 0) so set them equal to each other.





There are 2*pi radians in 1 revolution so:

So you need about 30 RPM to keep people from falling out the bottom