Very brief explanation please? - Newt 2nd Law w/ Circular Motion

[mc8569]

Consider a conical pendulum with a weight on it and that makes some angle with the vertical. I am told to find the radial acceleration of the weight and someone showed me how it is solved but I don't understand why:

I am told to set

Tsin@ = m(ar) *ar = radial acceleration
ar = (Tsin@)/m

I was wondering why it would be T*SIN* instead of T*COS*? Tcos@ would give you the force that is parallel with radial acceleration, Tsin@ gives you a force that is perpendicular to the radial acceleration... Please help me! I don't understand this - only should take a few seconds. Thanks! XP

 

[mc8569]

AHHHH OHHH NEVERMIND! Sorry... *CONICAL* pendulum, lol I was thinking of a regular, 2-D pendulum. I would delete this if I could, but I can't =\ But no need to respond anyone! So silly!

 

[kerimek]

The reason for using T*sin@ instead of T*cos@ is because in circular motion, the acceleration is always perpendicular to the velocity. In this case, the weight on the conical pendulum is moving in a circular path and the acceleration is directed towards the center of the circle. The tension force, T, is acting at an angle @ with respect to the vertical, but only the component of T that is perpendicular to the radial acceleration, which is T*sin@, is responsible for causing the circular motion. The component of T that is parallel to the radial acceleration, which is T*cos@, does not contribute to the circular motion and is therefore not used in the equation. I hope this helps clarify the reasoning behind using T*sin@ for finding the radial acceleration in this scenario.