Rotational acceleration Physics

Question

One end of a cord is fixed and a small 0.250-kg object is attached to the other end,
where it swings in a section of a vertical circle of radius 1.50 m as shown in the figure below. When θ = 16.0°,
the speed of the object is 5.00 m/s

 

Find the tension, radial and tangential components of acceleration.

 

I get confused when it comes to the acceleration, il try my best to explain.

 

I derived an expression for the tension

 

T= m(v²/r +g/cosθ) = 6.718 N

 

This is the total tension on the string.

 

I thought the radial acceleration would just be  a_r = v²/r

 

The net net force acting towards the middle of the circle would be  m(v2/r +g/cosθ) - mgcosθ (component of weight)

 

I was then thinking the radial acceleration would be  a_c = net radial force / mass

 

This would give (m(v2/r +g/cosθ) - mgcosθ)/m =  17.44 ms^-2

 

Using ar = v2/r = 16.6 17.44 ms^-2

 

Which one of these is correct for radial acceleration and why? Also would this be a negative answer?

Answer 1

You are correct, Ian.  The v²/r term is radial acceleration, not tangential.

 

How is the angle θ being measured?  With respect to what?  I would have to know that before being able to compare to your result.

Answer 2

I would use  a_r = v²/r    for the tangential acceleration.  This is because this acceleration moves linearly at all points of rotation.  Also, this linear acceleration is the same at all points of rotation.  Recall the typical free-body diagram of centripetal motion.

 

I would use the equation you used that involves the angle for radial acceleration.  This is because acceleration here is fixed about the center of the circle.