Download AP Physics Chapter 8.1 Notes

AP Physics Chapter 8.1 Notes
TORQUE
The tendency of a force to rotate a body about some axis is measured by a quantity called the
torque. We can find the magnitude of the torque by using the formula:
τ = Fd
where τ is the torque, d is the distance of the lever arm, and F is the force. The lever arm is the
perpendicular distance from the axis of rotation to a line drawn along the direction of the force.
EXAMPLE:
1.0 m
d2
F1=500 N
d1
Question: Find the net torque exerted on the crate
if its width is 1.0 m. Assume an axis of rotation
is through the center of the crate.
O
F2=500 N
Solution: The torque produced by F1 is
τ1 = F1d1 = -(500N)(0.50m) = -250 Nm
*A top view of a packing
crate being pushed with
equal but opposite forces.
and the torque produced by F2 is
τ2 = F2d2 = -(500N)(0.50m) = -250 Nm
Because each force produces clockwise rotation,
the torques are both negative. Thus, the net
torque is -500 Nm.
Chapter 8 Section 2
Torque and the Second condition for Equilibrium:
First Condition of Equilibrium: object has no net external force acting on it. ∑F x = 0 and ∑Fy = 0.
With the First condition we found that the object would stay at rest or move at a constant
velocity, yet this condition doesn’t truly guarantee that an object is in equilibrium. There is a
second factor or condition that needs to be fulfilled, the Second Condition for Equilibrium.
The Second condition for Equilibrium: if an object is in rotational equilibrium, the net torque on
it about any axis must be zero. ∑τ = 0.
Now we know that a body/object in static equilibrium must satisfy two conditions:
1. The resultant external force must equal zero. ∑Fnet = 0
2. The resultant torque must equal zero. ∑τ = 0.
F1 = 500N
An example to better clarify:
In this example we satisfy the First Condition
of Equilibrium because there are equal and
opposite forces acting on the crate. Although
Crate
the two forces are equal and opposite they
are not acting on the crate trough a common
point. Because of this irregularity the crate
will spin.
F2 = 500N
Position of Axis
When having to choosing an axis of rotation for calculations, the location of the axis is subjective, that is
if the object in question is in equilibrium.