Newton’s Second Law for Rotation Examples 1. The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 10 4 kgm 2 , and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s? F m 4 . 2
Newton’s Second Law for Rotation Examples 1.The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door.
Jan 01, 2016
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Newton’s Second Law for Rotation Examples
1. The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 104 kgm2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s?
F
m 4.2
Newton’s Second Law for Rotation Examples
1. The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 104 kgm2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s?
F
m 4.2
I I ?
Newton’s Second Law for Rotation Examples
1. The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 104 kgm2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s?
F
m 4.2
?
.90o rado 2.90
st .30
srad
o 0
Since the force and therefore the torque are constant, the resulting angular acceleration is
uniform. Hence, the rotational kinematic equations can be applied.
Newton’s Second Law for Rotation Examples
1. The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 104 kgm2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s?
F
m 4.2
?rado 2.90
st .30
srad
o 0
2
21
ttoo
2
2
to
2.302
2
s
rad
231049.3
srad
Newton’s Second Law for Rotation Examples
1. The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 104 kgm2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s?
F
m 4.2
231049.3
srad I
I
IRF .90sin
RI
F
m
sradkgm
F 4.2
1049.3107.8 2324
NF 130 lbs 28
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
1F
2F
3F
4F
1R
2R
net1 2 3
0
4 Inet
Inet
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
net1 2 30.80 Nm
0
4 sinrF
90sinrFrF
121 FR
Nm 0.612.01
Nm72.01
0.72
222 FR
Nm 0.412.02
Nm48.02 0.48
-0.80 Nm
1 2 3
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
net0.80 Nm
0
sinrF
90sinrFrF
313 FR
Nm 0.2050.03
Nm10.03 0.48
-0.80 Nm
0.10
1 2 3 41 2 30.72
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
net0.80 Nm
0
321 net
NmNmNmnet 10.048.072.0
Nmnet 14.0
0.48
-0.80 Nm
0.10
0.14
1 2 3 41 2 30.72
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
2
21
MRI 1F
2F
3F
4F
1R
2R 212.00.221
mkgI
20144.0 kgmI
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
Inet 1F
2F
3F
4F
1R
2R Inet
20144.0
14.0
kgm
Nm
Units:
2kgm
Nmkgm
skgm
kgm
Nm 2
2 2srad
Newton’s Second Law for Rotation Examples
2. A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F1 = 6.0 N, F2 = 4.0 N, F3 = 2.0 N, F4 = 5.0 N. Also, R1 = 5.0 cm and R2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.
1F
2F
3F
4F
1R
2R27.9
srad
Clockwise
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