Rotational Mechanics: Torque
Physics
Objectives:
• Define and describe torque
• Explain the use of net torque in determining if an object will rotate
• Describe the condition for one torque to balance another
6. Torque
- To make an object rotate, we must apply a force at a certain distance away from the axis
Example: opening a door
- Torque is a measure of the ability of a force to rotate an object around an axis.
Torque is defined as τ = r×Fsinφ
Axis
F
φ
r
Torque will be maximum when φ=90°. That is
rotation of the object will occur best(easier) when a
force is applied at an angle of 90°
This is the reason why the doorknob is positioned as
far away from the ‘axis’(hinge of the door) as
possible.
We choose counter-clockwise as positive direction
r is often referred to as the lever arm
Units of torque: Since torque is the product of Fsinφ (newtons) and r (meters), the unit for
torque is the newton-meter (N m).
(Note that this is similar to the unit of work which was the product of force and distance.
However, Joules are not used to specify torque. We will simply use newton-meters.)
Q1) Calculate the torque produced by a 50N perpendicular force
at the end of a 0.2m long wrench.
a) -8N·m
b) -10N·m
c) -12N·m
d) -14N·m
0.2m
Push with 50N of force!
1
0.5m
Q2) Calculate the torque produced by a 50N perpendicular
force at the end of a 0.5m long wrench.
a) -18N·m
b) -22N·m
c) -25N·m
d) -35N·m
Push with 50N of force!
Net Torque
There can be more than one torque acting on an object. (recall net force=>∑F=ma)
where τn = r×Fsinφ
∑τ =τ1 + τ2 + · · · τn
If the sum of the torques is zero, then there is no rotation.
F=10N
Q3) A meter-stick is pivoted at the center. Any
unbalanced torque will result in rotation of the
meter-stick. If a pushing force of 10N is applied at
each end of the meter stick (as shown), find the net
torque acting on the system. (and which direction:
clockwise or counter-clockwise?)
a) -10N·m
b) -15N·m
c) -20N·m
d) -25N·m
F=10N
Q4) A meter-stick is pivoted at the center. Any
unbalanced torque applied will result in rotation of
the meter-stick. If 15N and 10N forces are applied
as shown at the ends, find the net torque acting on
the system. (and which direction: clockwise or
counter-clockwise?)
a) 1.0N·m
b) 1.5N·m
c) 2.0N·m d) 2.5N·m
F=15N
F=10N
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Q5) A meter-stick is pivoted at the center. Any
unbalanced torque applied will result in rotation of
the meter-stick. If 15N, 10N and 5N forces are
applied as shown, find the net torque acting on the
system. The 10N force is applied 0.25m away from
the center (also find the direction: clockwise or
counter-clockwise?)
a) 1.0N·m
b) 1.5N·m
c) 2.0N·m d) 2.5N·m
Q6) A string is tied to a doorknob 0.79m from the
hinge as shown(top-view of a door). The force
applied to the string is 5N. What is the torque on
the door?
a) 3.3N·m b) 2.2N·m c) 1.1N·m d) 0.8N·m
F=15N
F=10N
hinge
F=5N
F
57°
3
Q7) One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane
parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick
in such a way that the net torque is zero. One force has a magnitude of 2 N and is applied
perpendicular to the length of the stick at the free end. The other force has a magnitude
of 6 N and acts at a 30 deg angle with respect to the length of the stick. Where along the
stick is the 6 N force applied? Express this distance with respect to the end that is
pinned.
ans: 0.667 m
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