Slipping & Sliding (College Board AP® Physics 1: Algebra-Based)

Study Guide

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Slipping and sliding refer to situations in which two surfaces are moving relative to each other
- Sliding occurs when two surfaces in contact move relative to each other and kinetic friction applies
- Slipping is a special case of sliding and occurs when an object that normally rolls does not, as covered in the study guide on Rolling

Static friction applies to an object that is rolling
- Considering a rotating bike wheel, each point on the wheel makes contact with one point on the road as it rolls along

Slipping occurs when an object moves translationally but without rotation, so it does not roll
- When the brakes are applied hard to a bike wheel the surface of the wheel slides over the ground and kinetic friction now applies
- The center of mass of an object moves faster translationally than the point of contact with ground

Static friction adopts the value and direction required to prevent an object from slipping or sliding on a surface

There exists a maximum value for which static friction will prevent an object from slipping on a given surface

$|{\vec{F}}_{f, s, m a x}| = |μ_{s} {\vec{F}}_{n}|$

Step 1: Identify the fundamental principle

$|{\vec{F}}_{f, s}| ⩽ |μ_{s} {\vec{F}}_{n}|$

Where:
- $|{\vec{F}}_{f, s}|$ = magnitude of static friction, measured in newtons $N$
- $μ_{s}$ = coefficient of static friction
- ${\vec{F}}_{n}$ = normal reaction force between the two contact surfaces, measured in newtons, in $N$

Step 2: Apply the specific conditions

The magnitude of static friction applied on an object increases until it reaches the point of slipping
When an object is right on the point of slipping static friction is at its maximum magnitude
- Equal in magnitude and opposite in direction to any applied force
The inequality means that the maximum value of static friction is equal to the product of the coefficient of static friction and the normal force
It is not possible for the magnitude of static friction to be greater than the product of the coefficient of static friction and the normal reaction force because this would mean
$|{\vec{F}}_{f, s}| > applied force$
- The object would then move in the direction of the static friction

the (exam) results speak for themselves:

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