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