Chapter 6 Rotation
Static Torque Balance
Torque
In comparison to force, torque is the
measurement of a force to rotate an object about an axis. Its mathematical
formula is:
Magnitude of Torque 
To find the
direction of torque, use the right hand rule.
1.
In
static horizontal forces must be balanced (
vertical
forces must be balanced
and torques must be balanced
.
2.
An
easier way to balance torques is to determine a pivot point and set counter
clockwise torques equal to clockwise torques.
Examples:
1. If
a torque of 55.0 Nm is required and the largest force that can be exerted by
you is 135 N, what is the length of the lever arm that must be used?
Answer:
2. Two
baskets of fruits hung by strings go around pulleys of different diameters as
shown below. What is the mass of basket A?
Answer: 
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3.
A light is suspended from a horizontal,
suspended pole as shown in figure. The pole is 2.10 m long and weighs 175 N.
The light, which weighs 105 N, is suspended 1.80 m from the left sidewall.
What is the tension of the cable supporting the pole? Answer: Draw a free body
diagram that includes all of the forces on the pole and set:
Select axis of rotation as the pivot
point.
T can be solved by using torque balance. 2.1× From above equation, solve for T. T = —420 N(upward) |
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4.
A pivoted[AC1]
lamp pole is shown in figure. The
pole is 0.44 m long and weighs 27 N. The lamp weighs 64 N and is located 0.33
m from the left sidewall. a. What
is the torque caused by the weights of lamp and pole? Answer: Select axis of rotation as the pivot point.
b.
Determine the tension of the rope
supporting the lamp pole. Answer: Draw a free body diagram that includes all
of the forces on the pole and set: Select axis of rotation as the pivot point.
T = —64 N (upward) |
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5.
The bar is 20 kg and 10 m long. Find the
tension of the cable, and both the horizontal and vertical components that
the hinge supplies to the bar. Answer: Draw a free body
diagram that includes all of the forces on the pole and set:
Select the hinge as the pivot point.
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6.
A 10-meter-long ladder leans against the
wall as shown in figure. If the ladder weighs 100 N, what is the minimum
value of the static friction coefficient, μmin? Answer: Draw a free body
diagram with all the forces on the pole and set:
Select ground as the pivot point.
μmin = 0.375 |
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7.
A 10-meter-long ladder leans against the
wall as shown in figure. If the ladder weighs 400 N and Answer: Draw a free body diagram that includes all
of the forces on the pole and set:
Select ground as the pivot point.
Use equations (1),
(2), and (3) to solve:
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The center of mass of a distributed mass in space is the
unique position where the sum of the mass
multiplying its relative position is equal to zero.
Example: How far to the right of point A should a
fulcrum/support be placed in order
to balance the object?
Answer: 
,
divided into three blocks, with centers at 2, 6, and 12 cm from point A,
respectively
from point A