#1 A horizontal vinyl record rotates freely about a vertical axis through its center with an angular speed of 5 rad/s. The rotational inertia of the record about its axis of rotation is 5 x 104 kg m\'2, the mass of the record is 200 g. A wad of wet putty of mass 0.02 kg drops vertically onto the record from above and sticks to the edge of the record. What is the angular speed of the record immediately after the putty sticks to it? #2 a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. b) Calculate the magnitude of the angular momentum of the earth due to its rotation around its axis through the north and south poles.
Solution
#1
Given
mass of record M = 200 g = 0.2 kg
angular speed of record wi = 5 rad/s
the rotational inertia of the record I = 5*10 -4 kg*m 2
mass of putty m = 0.02 kg
By using law of conservation of angular momentum
Li = L f
(I*wi) record + 0 = (I + mr 2 )w f
5*10 -4 *5 = (5*10 -4 + 0.02*(0.1) 2 ) w f
25*10 -4 = 7*10 -4 *w f
w f = 3.57 rad/s
#2
(a)
The expression for angular momentum is,
L =I*w ............(1)
The expression for moment of inertia for circular path is,
I =m*r 2
The expression for angular speed is,
w = v/r
from equation (1)
L = (m*r 2 )*(v/r)
L = m*v*r
Radius of the circular orbit is r = 1.50*10 11 m
Mass of the earth is m = 5.97*10 24 kg
Speed of the earth around the sun is v = 2.98*10 4 m/s
L = 5.97*10 24 * 2.98*10 4 *1.50*10 11
L = 26.68*10 39 kg*m 2 /s
(b)
L = I*w
where I = 2/5*m*r 2
w = 2*pi/T
L = (2/5*m*r 2 )*(2*pi/T)
Radius of the earth is r =6.38*10 6 m
Mass of the earth is m = 5.97*10 24 kg
T = 24 hr
L = [ 2/5 *5.97*10 24 *(6.38*10 6 ) 2 ]*[2*3.14/24*3600]
L = 7.06*10 33 kg*m 2 /s
.
Measures of Dispersion and Variability: Range, QD, AD and SD
#1 A horizontal vinyl record rotates freely about a vertical axis thro.docx
1. #1 A horizontal vinyl record rotates freely about a vertical axis through its center with an angular
speed of 5 rad/s. The rotational inertia of the record about its axis of rotation is 5 x 104 kg m'2,
the mass of the record is 200 g. A wad of wet putty of mass 0.02 kg drops vertically onto the
record from above and sticks to the edge of the record. What is the angular speed of the record
immediately after the putty sticks to it? #2 a) Calculate the magnitude of the angular momentum
of the earth in a circular orbit around the sun. b) Calculate the magnitude of the angular
momentum of the earth due to its rotation around its axis through the north and south poles.
Solution
#1
Given
mass of record M = 200 g = 0.2 kg
angular speed of record wi = 5 rad/s
the rotational inertia of the record I = 5*10 -4
kg*m 2
mass of putty m = 0.02 kg
By using law of conservation of angular momentum
Li = L f
(I*wi) record + 0 = (I + mr 2
)w f
5*10 -4
*5 = (5*10 -4
+ 0.02*(0.1) 2
) w f
25*10 -4
= 7*10 -4
*w f
w f = 3.57 rad/s
#2
2. (a)
The expression for angular momentum is,
L =I*w ............(1)
The expression for moment of inertia for circular path is,
I =m*r 2
The expression for angular speed is,
w = v/r
from equation (1)
L = (m*r 2
)*(v/r)
L = m*v*r
Radius of the circular orbit is r = 1.50*10 11
m
Mass of the earth is m = 5.97*10 24
kg
Speed of the earth around the sun is v = 2.98*10 4
m/s
L = 5.97*10 24
* 2.98*10 4
*1.50*10 11
L = 26.68*10 39
kg*m 2
/s
(b)
L = I*w
where I = 2/5*m*r 2
w = 2*pi/T
L = (2/5*m*r 2
)*(2*pi/T)
Radius of the earth is r =6.38*10 6
m
Mass of the earth is m = 5.97*10 24
kg
T = 24 hr
3. L = [ 2/5 *5.97*10 24
*(6.38*10 6
) 2
]*[2*3.14/24*3600]
L = 7.06*10 33
kg*m 2
/s
