An anemometer for measuring wind speed consists of four metal cups, each of mass
ID: 1286848 • Letter: A
Question
An anemometer for measuring wind speed consists of four metal cups, each of mass m = 129 g, mounted on the ends of four essentially massless rods of length R= 0.29 m. The rods are at right angles to each other and the structure rigidly rotates at f = 12 rev/s. Treat the cups as point masses.
1)
What is the moment of inertia of the anemometer about the axis of rotation?
I =
2)
What is the angular momentum of the anemometer about the rotation axis?
L =
3)
A small block of mass 0.91 kg slides without friction on a horizontal table. Initially it moves in a circle of radius r0 = 0.63 m with a speed 1.5 m/s. It is held in its path by a string that passes through a small hole at the center of the circle. The string is then pulled down a distance of r0 - r1 = 0.12 m, leaving it at a radius of r1 = 0.51 m. It is pulled so slowly that the object continues to move in a circle of continually decreasing radius.
How much work was done by the force to change the radius from 0.63 m to 0.51 m?
W =
Explanation / Answer
1)
I = 4*m*r^2
= 4*0.129*0.29^2
= 0.0434 kg.m^2
2)
w = 12*2*pi rad/s
= 75.36 rad/s
L = I*w
= 0.0434*75.36
= 3.27 kg.m^2/s
3)
here angular momentum of puck is conserved
L1 = L2
m*vo*ro = m*v1*r1
v2 = vo*(ro/r1)
= 1.5*( 0.63/(0.63-0.12) )
= 1.85 m/s
Workdone = chnage in kinetic enrgy
= 0.5*m*(v1^2-vo^2)
= 0.5*0.91*(1.85^2-1.5^2)
= 0.533 J