1) Introduction

Friction is the force that opposes relative motion or the tendency of relative motion between two surfaces in contact.
It acts tangentially to the surfaces in contact.

2) Types of Friction

• Static Friction: Acts when a body is at rest, preventing motion.
• Limiting Friction: Maximum value of static friction, just before the body starts sliding.
• Kinetic (Sliding) Friction: Acts when a body slides over another surface; usually less than limiting friction.
• Rolling Friction: Acts when a body rolls over a surface (much smaller than sliding friction).

3) Laws of Friction

1. Friction always opposes relative motion.
2. Magnitude of static friction \(f_s\) adjusts itself up to a maximum value (limiting friction).
3. Limiting friction is directly proportional to the normal reaction:
   \[
   f_{max} = \mu_s N
   \]
4. Kinetic friction is nearly constant and proportional to normal reaction:
   \[
   f_k = \mu_k N
   \]
5. Generally, \(\mu_k < \mu_s\).
6. Friction depends on the nature of surfaces, not on the area of contact (ideally).

4) Limiting Friction & Coefficient of Friction

Limiting friction: The maximum static friction before motion begins.
Coefficient of friction (\(\mu\)): The ratio of limiting friction to normal reaction:

\[
\mu = \frac{f_{max}}{N}
\]

It is a dimensionless quantity.

5) Angle of Friction & Angle of Repose

• Angle of Friction (\(\phi\)): The angle between the resultant of normal reaction \(N\) and limiting friction \(f_{max}\) with the normal to the surface.
  \(\tan\phi = \mu\).
• Angle of Repose (\(\theta_r\)): The minimum angle of incline at which a body just starts sliding down.
  \(\tan\theta_r = \mu\).
• Thus, \(\theta_r = \phi\).

6) Rolling Friction

When a body (like a wheel, cylinder, or ball) rolls over a surface, friction at the point of contact is much smaller compared to sliding.
This is why wheels are used in vehicles.

7) Work Done by Friction

Work done by friction:
\[
W = f \cdot d \cdot \cos 180^\circ = -f d
\]
(since force of friction is opposite to displacement).
⇒ Friction usually does negative work, dissipating energy as heat.

8) Applications of Friction

• Walking is possible due to static friction between feet and ground.
• Brakes in vehicles work due to friction.
• Nails and screws hold due to friction.
• Writing on a blackboard/paper requires friction.
• Excessive friction causes wear and tear → lubricants reduce it.

9) Solved Examples

10) Practice Questions

1. A 5 kg block rests on a horizontal floor. If \(\mu_s=0.5\), find limiting friction. (Take \(g=9.8\)).
2. Differentiate between static, kinetic and rolling friction with examples.
3. A block starts sliding down an incline at \(37^\circ\). Find coefficient of friction.
4. Why is it easier to roll a body than to slide it?
5. Explain how lubricants reduce friction.

11) Answer Key

1. Normal = 5×9.8 = 49 N. Limiting friction = 0.5×49 = 24.5 N.
2. Static = prevents motion, Kinetic = opposes sliding, Rolling = opposes rolling. (Give examples).
3. \(\mu = \tan 37^\circ \approx 0.75.\)
4. Rolling friction is much less than sliding friction, so easier.
5. They fill irregularities, reduce interlocking of surfaces, hence reduce friction.