Torque and Circular motion with banks Flashcards
Always remember that in any circular motion, the net force is equal to the centripetal force.
Facts
What is the formula for friction force?
Friction force
= Friction Force coefficient x Normal Force
F = μR
Where μ is the friction coefficient
R is the normal force (equivalent to mg, unless it is upside down or not in a normal stationary ground position)
What is friction force equal to in circular motion? What kind of friction force is it?
Also, what does the R stand for in the context of circular motion?
Friction Force is equal to the Centripetal Force in a circular motion. Note that the centripetal force is also equal to the net force.
The friction force evident in a circular motion, can be thought of the sideways friction force, which pushes the objects towards the centre of the circular, making it go inwards and circular every time.
Therefore,
friction force = Net force = Centripetal Force
‘R’ is the reaction force, but still can be considered to be the normal force
In formula terms, what is the derivation of friction force = Centripetal force?
μR = mv^2/ r
Where r is the radius/ ‘distance’ in meters
R is the normal force
In a roller coaster, where is the normal force, if the carriage is upside down and hanging on a circular track below the bar?
The normal force would be downwards, in the same direction and magnitude as the weight force.
This is because the normal force is always perpendicular to the surface or ground. In this case, the surface is on top of the carriage and therefore, the normal force is downwards.
Therefore, the net force of the vertical component is twice the weight force, or the downward force of R + mg
What is banking and what effect does it have on the frictional force or circular motion in general?
Banking in Physics is the process in which a surface is elevated at a particular angle at a turn on the surface
Banking reduces the need for sideways frictional force and allows cars or bicycles to travel faster without skidding off the road or away from the circular path
Therefore, banking eliminates sideways friction force.
In a banked situation, think of those bicycle Olympic situations, where there is a constant curve.
In this instance, there is always an elevated normal force (depending on the angle of the bank) and a weight force. The net force would be the centripetal force of htese two, which pushes the car ot bicycle inwards.
As a result, the angle of the ramp or ‘bank,’ can be obtained by?
Tan theta = Net force / Weight force
Derive the formula by expanding net force/ centripetal force formula and weight force formula
you will get mv^2/r divided by mg
Therefore, the angle of elevation of the bank is:
Tan theta = v^2 / rg
where r is the radius in meters
