Download Lever Arm

Causing Rotational Motion
• In order to make an object start rotating
about an axis, a force is required
• However, not only the amount of force
applied but also the position from the axis
to which it is applied is important in
determining the amount of rotation (angular
acceleration
• Distance from axis is called the Lever Arm
Torque Definition
• Combination of amount of force and
distance from axis is called Torque (τ)
• A torque is necessary in order to provide
angular acceleration
• τ = rF
r- dist from axis
• Units - N m
• In order to use this equation, the force must
be perpendicular to the axis of rotation
Example 1
• A biceps muscle exerts a vertical force on
the lower arm as shown. Calculate the
torque acting on the lower arm if the muscle
is attached 5.0 cm from the elbow.
Example 2
• A wrench is pulled by a force of 30 N at an
angle of 30° with the axis and a distance of
15cm from its pivot end. What torque is
acting on it?
Equilibrium
• Occurs when total force acting balance and
no rotational motion occurs
• In order for equilibrium to exist, the total
torque acting in the clockwise direction
must balance the total torque acting in the
counterclockwise direction
See-Saw
• When stationary, the total τ clockwise is
equal to the τ counterclockwise
• If kid A pushes up with more force, the τ is
no longer balanced (more force clockwise)
and the see-saw begins to rotate clockwise
with an angular velocity
Example 3
• Two people are sitting on a seesaw that is
2.5 m long. One has a mass of 40 kg and the
other a mass of 60 kg. Where would the
support on the see-saw need to be placed in
order to produce equilibrium?
Example 4
• A 7.0 m beam is hanging from the ceiling
by two ropes on its ends. The bar has a mass
of 300 kg and it is non-uniform, with its
center of mass 3.0 m from one end. A 400kg
mass is hung from the beam’s light end and
a 200 kg mass is hung from its heavy end.
What force is acting on each rope?