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Mechanics tutorial_5.doc
1
1.
For a cylinder of radius a, mass M, and length L, determine (a) the moment of inertia about
the axis of the cylinder and (b) moment of inertia about an end diameter.
ans:
(a) Ma
2
/2
(b) M(a
2
/4 + L
2
/3)
2.
The diagram shows a drum of cylinder radius r and flank radius R. If the cable is horizontal
and the friction between the ground and the drum is sufficient to prevent slip, what is the
acceleration of the drum given tension in cable is T. Discuss the direction of motion when
the drum starts from rest. Mass of drum is M, moment of inertia about drum axis is I
G
.
r
R
T
cable
ans:
T(1r/R) / (M + I
G
/R
2
)
3.
The diagram shows two pulleys, P
1
and P
2
, connected by a belt. The effective radius of P
2
is r and its axial moment inertia is I. The system is initially at rest and the tension in the belt
is T
o
. The motor M which drives the pulley P
1
is then started and it may be assumed that
the average tension T
AB
and T
CD
in sections AB and CD of the belt remains equal to T
o
.
Denoting the anticlockwise angular acceleration of pulley P
2
by
and the clockwise
resisting couple on the same axle by Q, find expressions for T
AB
and T
CD
, neglecting mass
of the belt.
A
B
P
P
2
1
D
C
M
ans:
T
o
+(I
+Q)/2r, T
o
+(I
+Q)/2r
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2
4.
The diagram shows a hoist consists of a winding drum D driven by an electric motor M. A
pinion of N
M
teeth on the motor shaft meshed with a gear wheel of N
D
teeth attached to the
drum. The effective radius of the drum is R. The total axial moment of inertia on the drum
shaft is ID and on the motor shaft is I
M
. The rope wrapped around the drum carries a load
of mass m at its lower end which is being raised with an acceleration a. Neglect bearing
friction and the mass and stretch of the rope; determine the couple being applied to the rotor
of the motor.
a
M
Drum D
Pinion
ans:
Rmg
R
a
mR
N
N
I
I
N
N
C
M
D
M
D
D
M
M
2
2
5.
An experimental vehicle powered by a jet engine whose thrust can be represented by the
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 Spring '09
 GXXY

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