Tangential Acceleration

heartyface

*I am reposting as I previously posted this in the wrong category.

1. The problem statement, all variables and given/known data
Perhaps I am confused by the concept.
A toy car starts from rest at a height 4R above the ground and continue to a loop of radius R (frictionless). At a point C (height R from the ground) inside the loop, what is the tangential acceleration of the toy car?


2. Relevant equations

I don't think a=alpha*r is quite relevant to this...or a=dv/dt...

3. The attempt at a solution
not quite yet. perhaps the gravity is the only thing?

Please, explain me of the concept of 'tangential acceleration' and its components.

SammyS

'Tangential acceleration' is the component of acceleration that is in the direction of the motion, i.e., it's in the direction tangential to the path which the object is taking. It can also be said that it is the component of acceleration that is in the direction of the velocity vector.

MrWarlock616

Do you have a diagram to the question that you can attach?

tiny-tim

hi heartyface!

to add to what SammyS has said …
… for constant r, both are correct!

(yes, it really is that simple! )

heartyface

Does that mean gravity, of which according to the diagram shows that the car is moving 'vertically' at that moment, is also a part of the tangential acceleration?

Mr. Warlock- here it is

Tiny Tim- really? how would I use such equations in this problem?

SammyS

Yes, the acceleration due to gravity is very involved.

Draw a free body diagram for the car at point C.

What force besides gravity, if any, is acting in the vertical direction, on the car at point C ?

Attached Thumbnails

 

tiny-tim

no, acceleration (like distance and speed) is geometry

(and force is physics, and gravity is a force)
presumably you'll be finding either θ or ω as a function of t …

so differentiate to find α, then multiply by R

heartyface

I see, thanks guys, but what if
?
What will the tangential acceleration be at each points?
At C, it is mere g acting against the motion of the car
At A, it is g acting in favor of the motion of the car.
However, and B and D, g is not in the direction in the tangential motion- does that mean there is no tangential acceleration at points B and D?

SammyS

I would say more explicitly that the tangential acceleration at points B and D is zero.

heartyface

^ I see, that clears it up. thanks Sammy :)