Physics dictates that dynamic friction is a force applied based on two parameters:

• The coefficient of friction between two given materials (determined experimentally)
• The amount of force between the two objects

The relative velocity of the two objects is not present in this equation.

In practice, it's quite possible you're generating extra heat and causing friction fade (the coefficient of friction is often temperature dependent), actually reducing the amount of force/torque applied to the input shaft of the transmission.

The reason you add throttle is:

• Add energy to the flywheel
• Get the engine into a range where it can generate more torque without stalling

Thus allowing you to be more aggressive on the clutch.

Obligatory: Don't hold a car on a hill for long periods using the clutch

Physics dictates that dynamic friction is a force applied based on two parameters:

• The coefficient of friction between two given materials (determined experimentally)
• The amount of force between the two objects

The relative velocity of the two objects is not present in this equation.

Edit: that equation is very simply

F_d = u_d * F_n Where

• F_d is the dynamic friction force
• u_d is the coefficient of dynamic friction between the two surfaces
• F_n is the normal force. The amount of force applied perpendicular to the interface between the two surfaces

In practice, it's quite possible you're generating extra heat and causing friction fade (the coefficient of friction is often temperature dependent), actually reducing the amount of force/torque applied to the input shaft of the transmission.

The reason you add throttle is:

• Add energy to the flywheel
• Get the engine into a range where it can generate more torque without stalling

Thus allowing you to be more aggressive on the clutch.

Obligatory: Don't hold a car on a hill for long periods using the clutch

Additionally: u_d is a complicated thing, which is why it's easiest to determine it experimentally. Things that can affect it:

• temperature
• glazing (overheating causes a layer of much lower friction material to develop. This can sometimes cost the clutch)
• Water/oil presence (though this is no longer a dry u_d so one could argue this)