TURNING CORNERS AND CIRCLING

When cars/bikes/persons/skiers turn a corner they are all changing their motion if not their speed.

The direction of travel changes.

They are accelerating - and subject to an unbalanced force.

Newton's Second Law applies. Acceleration takes a broader meaning.

Consider the ball approaching the hockey stick and being hit into a new direction. The hit takes a certain time, Δt.

When the ball leaves the hockey stick, it has a new direction and possibly a new speed ( then again, maybe not! ).

The CHANGE IN MOMENTUM Δp, is the crucial thing as usual!

Remember that

Inital momentum p_initial plus (+) the Change Δp gives (=) the Final momentum p_final
( Ball comes, hit it , gives final momentum )

Thus Change in Momentum = Final momentum - Initial momentum

Δp = p_final - p_initial

We must do a vector subtraction.

Reverse the direction of the Initial momentum to give the negative and then do the geometry ( cos rule etc ) needed.

The change in momentum must have the same direction as the hit the unbalanced force because

F_unbal = Δp / Δt

Notice the direction of the force by the hockey stick ( the unbalanced force on the ball ) ! It agrees with the direction of the whack the stick gave on the ball ( as it should ! ) and the change in momentum.

If we now "dribble" the ball around in a circle - we need to continuously provide forces like the above hit to the ball to make it follow the circular direction. The taps on the ball will always be INWARDS towards the centre of the circle we are creating.

To make something go in a smooth circle, the inward force must be continous.

Exercise:

Identify the actions you need to take to go around a corner if you are

rollerblading

skateboarding

flying

playing hockey

riding a bike

skiing ( water or snow )

In all these activities you will need to create a new, not cancelled, force inwards on you to turn yourself.

Regardless of cause of the force, it is given the name CENTRIPETAL FORCE meaning "towards circle centre".

When we study the change in momentum through geometry, we find that

if the circle created has radius r, and speed of v, with a mass of m

then UNBALANCED FORCE causing all this has size

F_unbal = mv²
r

and the acceleration felt will be a = v² / r

***
Your perception when turning a corner is that you will be "thrown outwards" , that some mysterious force wants you out of the circle. Simply, you are responding to your initial momentum continuing you on your original direction.

This nonexistent force is often quoted as the "centrifugal force" even by top physicists. In the Newtonian world - thems wrong.