understanding the radial tangential coordinate system

Understanding the

Radial Tangential

coordinate system

Radial Axis

Is the line running from the suspension point along the string towards the

mass

Ө angle, radial axis makes with equilibrium

Two force components line on axis

Weight component : mgcosӨ

Tension component: T

Test Your Understanding

Which Arrow represent the radial

axis?

A

B

C

D

C

Test Your Understanding

What is the acceleration of the

mass along the radial axis?

A – in the opposite direction of T

(Tension force)

B – towards the suspension point

along the direction of T (Tension

force)

C – zero

C – remember the T (tension force)

and the weight component (mgcosӨ ) are equal and opposite!

Tangential Axis

Is perpendicular to the radial axis

Only one force component along this axis

Weight component: mgsinӨ

The Force is always in the direction of the equilibrium position

Test Your Understanding

Which direction is the force

of weight component along

the tangential axis?

A – towards the equilibrium

B – the direction is always towards

the left

C – the direction is always towards

the right

A

Bringing it together

What is the acceleration of

the mass at its equilibrium

position?

Zero! There is no motion along the

radial axis since force T (tension)

and the weight component on radial axis (mgcosӨ) cancels out.

Also since Ө=0 the force

component on the tangential axis

is zero (mgsin(0)=0). Since the net

force on the mass is zero there is

no acceleration at the equilibrium

position.