Phys 1L03 Tutorial session Set 7
Seventh series: Questions on Center of mass, and Torque
Concept:
1. Three masses, 2.0 kg, 3.0 kg, and 6.0 kg, are
located at points (3.0, 0), (6.0, 0), and (-4.0,
0), respectively, in meters from the origin.
Where is the center of mass of this system?
2. A dumbbell, Figure below, has a connecting bar of
negligible mass. Find the location of the center of
mass
a. if m 1nd m ar2 each 5.0 kg and
b. if m1 is.0 kg and m i2 10.0 kg.
3. A water molecule consists of an oxygen atom and two hydrogen
atoms. Oxygen has a mass of 16 atomic units (u) and each hydrogen
has a mass of 1 u. The hydrogen atoms are each at an average distance
of 96 pm ( 96 x 10 -12 m) from the oxygen atom, and are separated
from one another by an angle of 104.5 . Find the center of mass of a
water molecule.
4. Two children are balanced on a see-saw of negligible mass. (This assumption is made to keep the
example simple.) The first child, sitting on left side of the pivot, has a mass of 26.0 kg and sits 1.60 m
from the pivot. The second child, sitting on right side of pivot, has a mass of 32.0 kg and 1.3 m from the
pivot. Calculate the position of center of mass of the two children:
a. from the first child
b. from the pivot point.
5. Three balls A, B, and C, with masses of 3 kg, 1 kg, and 1 kg,
respectively, are connected by massless rods. The balls are located as
in Figure below. What are the coordinates of the center of mass?
6. Alley club-ax consists of a symmetrical 8 kg stone attached to the
end of a uniform 2.5 kg stick that is 98 cm long. The dimensions of
the club-ax are shown in Figure blow. How far is the center of mass
from the handle end of the club-ax? Phys 1L03 Tutorial session Set 7
Seventh series: Questions on Torque, and Levers
Concept:
Torque : is a tendency of a force to change the rotational motion.
Torque [τ] = (Force applied [F]) x (lever arm [r ⊥)
Where: the lever arm, r⊥,is defined as the perpendicular distance from the axis of rotation to the
line of action of the force.
Or:
τ = F r sinθ
τ = F r
⊥
τ = F r
⊥
Where: r ⊥is the lever arm and ⊥ isthe force component
perpendicular to the line of action of the force.
Lever: is a rigid bar (e.g. Bone) tha

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