Answer:
155.5 rev/min
Explanation:
First, we will calculate the initial moment of inertia I_o. We will consider the ice skater as a rod rotating around its axis. Then, we calculate the final moment of inertia I_f. In this occasion we consider the arms as a rod of length L that is horizontally positioned, L so that the length of an arm is L/2. We will call M_1 the mass that remains close to the rotation axis (90 percent) and M_2 the mass located at the arms (10 percent). Finally, we write the equation for the conservation of angular momentum and we solve for ω_f.
I_o=MR^2/2
=(45)(0.15)^2/2
=0.5 kgm^2
M_1=(0.9)(45)
=40.5 kg
M_2=(0.1)(45)
=4.5 kg
I_f=M_1*R^2/2+M_2*L^2/12
=1.1 kg m^2
I_f*ω_f=I_o*ω_o
ω_f = I_o*ω_o/ I_f
=155.5 rev/min
Weight is a force, so we use newtons second law which states F=ma. So the weight of a watermelon on earth is 2kg x 9.81m/s², which is 19.62N (newtons). On the moon it weighs 2 x 1.63 which is 3.26N.
The weight of the pen is 0.02 x 9.81, which is 0.1962N. If the pen is not to fall the frictional force needs to be equal to this force, so the answer is 0.1962N.
A ball rolling on a carpet!
To solve this problem, it is necessary to apply the concepts related to the change of entropy in function of the Volume in two states due to the number of moles and the ideal gas constant, this can be expressed as
Where,
R = Gas constant
V = Volume (at each state)
At the same time the number of moles of gas would be determined by the ideal gas equation, that is,
Where,
P = Pressure
V = Volume
R = Gas Constant
T = Temperature
Using the value of moles to replace it in the first equation we have
Therefore the correct option is A.