Torque
Learning Intention:
• To learn about what TORQUE is, and
• How to use torque to solve ROTATIONAL EQUILIBRIUM problems
Torque
• Torque is the turning effect of a force
where
T = torque (Nm)
r = radius of rotation (m)
F = force N)
Torque is also called a turning
moment, or sometimes just a
moment.
(clockwise moment)
In the diagram shown above, there is a
clockwise turning moment applied to
rotate the wrench.
Using Torque: Opening a door
• It’s easy to open a door when
you try to open it at the handle
end. This is because there is a
large radius (r ) to the rotation
point (the hinge).
• Ever tried opening a door by
pushing on it close to the
hinge? It’s much much harder!
• A much smaller r means you
need a much larger F to create
the same torque, T
• Spanners and other tools
work in a similar way.
r = large
small F needed to create same torque
(easy to open)
r= small
Large F needed to
create same
torque (much
harder to open)
Rotational Equilibrium
• If a system is in rotational equilibrium (balance), like a
see saw, for example,
anticlockwise torque = clockwise torque
• This principle is used in many torque problems.
Example: See Saw Problem
Johnny & Billy are sitting on a
see-saw 3.0m long. Billy is sitting
at the end.
Billy
Johnny
Mass 20kg
Mass 30kg
How far from X should Johnny sit
so the see-saw is balanced ?
Solution:
Torque
= torque
294 x d = 196 x 1.5
294d = 294
d = 1m.
X
d=?
30 x 9.8 = 294N
1.5m
20 x 9.8 = 196N
So because Johnny has a greater mass (& weight)
he should sit CLOSER to X to make the see-saw
balance.
Torque Worksheet
WORKED SOLUTIONS
Q19 solution
19. The two buckets shown in
figure 14.69 are lifted using a
stiff rod. How far from the
left-hand end should the rod
be picked up so that it
remains horizontal (assuming
the weight of the rod is
negligible)?
Q20 solution
Answer:
•As Sam walks past the pivot, the seesaw will move down
(rotate anticlockwise).
•This happens when Sam’s torque > torque from bag
Q21 solution
Ra
Answer
Rb
Note: an abutment is an end of the bridge where all the load is taken.
a) As truck goes from left to right, reaction force Ra ↓ and Rb ↑
In maths, in
simultaneous
equations, we
eliminate y to
solve for x.
In this question,
we eliminate RB
(by taking torques
from RB) to find RA
b)
Q21 solution (continued)
Q23 solution
Q24 solution
Q29
solution
Answer:
Q30 solution
(continued)
Q30 solution (continued)
Q32 solution
Q32 solution (continued)
Again, if you add up all the
downwards forces:
800N (man)
600N (woman)
200N (girl)
2000N (bridge)
Total 3600N
Then
Total forces down = total forces up
3600 = RA + RB
= 1766.6 + 1833.3
Again, once you know
RA, you can find RB by
subtracting RA from the
total forces downwards:
RB = 3600 – RA
= 3600 – 1766.3
= 1833.3N.
Q33 solution
Note: the centre of mass of the plank
can be taken to be acting in the
middle of its length (ie. 3m)
Q35 solution
Q36 solution