College Physics for AP® Courses

# Section Summary

### 9.1The First Condition for Equilibrium

• Statics is the study of forces in equilibrium.
• Two conditions must be met to achieve equilibrium, which is defined to be motion without linear or rotational acceleration.
• The first condition necessary to achieve equilibrium is that the net external force on the system must be zero, so that $netF=0netF=0 size 12{F rSub { size 8{ ital "net"} } =0} {}$.

### 9.2The Second Condition for Equilibrium

• The second condition assures those torques are also balanced. Torque is the rotational equivalent of a force in producing a rotation and is defined to be
$τ = rF sin θ τ = rF sin θ size 12{τ= ital "rF""sin"θ} {}$

where $ττ size 12{τ} {}$ is torque, $rr size 12{r} {}$ is the distance from the pivot point to the point where the force is applied, $FF size 12{F} {}$ is the magnitude of the force, and $θθ size 12{θ} {}$ is the angle between $FF size 12{F} {}$ and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm $r⊥r⊥ size 12{r rSub { size 8{ ortho } } } {}$ is defined to be

$r ⊥ = r sin θ r ⊥ = r sin θ size 12{r rSub { size 8{ ortho } } =r"sin"θ} {}$

so that

$τ=r⊥F.τ=r⊥F. size 12{τ=r rSub { size 8{ ortho } } F} {}$
• The perpendicular lever arm $r⊥r⊥ size 12{r rSub { size 8{ ortho } } } {}$ is the shortest distance from the pivot point to the line along which $FF size 12{F} {}$ acts. The SI unit for torque is newton-meter $(N·m)(N·m)$. The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero:
$net τ = 0 net τ = 0 size 12{"net "τ=0} {}$

By convention, counterclockwise torques are positive, and clockwise torques are negative.

### 9.3Stability

• A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement.
• A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.
• A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.

### 9.4Applications of Statics, Including Problem-Solving Strategies

• Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain. We have discussed the problem-solving strategies specifically useful for statics. Statics is a special case of Newton's laws, both the general problem-solving strategies and the special strategies for Newton's laws, discussed in Problem-Solving Strategies, still apply.

### 9.5Simple Machines

• Simple machines are devices that can be used to multiply or augment a force that we apply – often at the expense of a distance through which we have to apply the force.
• The ratio of output to input forces for any simple machine is called its mechanical advantage
• A few simple machines are the lever, nail puller, wheelbarrow, crank, etc.

### 9.6Forces and Torques in Muscles and Joints

• Statics plays an important part in understanding everyday strains in our muscles and bones.
• Many lever systems in the body have a mechanical advantage of significantly less than one, as many of our muscles are attached close to joints.
• Someone with good posture stands or sits in such a way that the person's center of gravity lies directly above the pivot point in the hips, thereby avoiding back strain and damage to disks.
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