Torque
Torque is an influence which tends to change the rotational motion of an object. One way to quantify a torque isTorque = Force applied x lever arm=F x rThe lever arm is defined as the perpendicular distance from the axis of rotation to the line of action of the force.
Torque
Torque
Torque
Equilibrium
Torque
Conditions for equilibrium1. The sum of all the forces (net force) acting on
an object is zero. 2. The sum of all the torques (net torque)
acting on an object is zero.
Torque
Mathematical notation
0
0
ii
ii
F
Torque
By convention1. Counterclockwise torque is
positive2. Clockwise torque is negative
Torque
Consider a board balanced on its center with masses hanging on each side of the center.
TorqueUse the following information.m1=1.0kgm2=1.0kgm3=3.0kgmboard=2.0kgL1=2.0mL2=1.0m1. What is the force exerted by the
fulcrum? 2. What is L3?
TorqueCalculating the forces1) There are no horizontal forces
0
0
ii
up down
F
F F
Torque
Because the board is balanced on its center its weight does not enter into the torque calculations.
Torque
We can actually select any point as the axis of rotation, but it is convenient to use the point below which the board is supported.
TorqueCalculating the torques
0i counterclockwise clockwisei
TorqueCalculating the torques
1 1 2 2 3 3
1 1 2 2 3 3
1 1 2 23
3
0
1.0 2.0 1.0 1.01.0
3.0
gm L gm L gm L
gm L gm L gm L
kg m kg mm L m LL m
m kg
Torque
Calculating the forces
1 2 3
1 2 3 2
0
9.81 1.0 1.0 3.0 2.0 67
i board fulcrumi
fulcrum board
F g m m m m F
mF g m m m m kg kg kg kg N
s