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## Homework Statement

A 0.4 kg object rotates in a vertical circle at the end of a 0.5 m string. What is the tension of the string at the bottom if the angular velocity there is 8.0 rad/s?

## Homework Equations

centripetal acceleration = R*w^2

weight = mg

R = radius of circle

w = angular velocity

## The Attempt at a Solution

centripetal acceleration = (0.5 m)(8.0/s)^2 = 32 m/s^2

total (centripetal) force = (0.4 kg)(32 m/s^2) = 12.8 N (upwards)

weight = (0.4 kg)(9.8 m/s^2) = 3.9 N (downwards)

Upwards forces and accelerations will be considered positive, downwards ones negative.

total (centripetal) force = string tension - weight

12.8 N = string tension - 3.9 N

string tension = 12.8 N + 3.9 N = 16.7 N

In general terms:

string tension = mg + mRw^2

Unfortunately, the "official" solution is 13 N.

Am I wrong, or are my course materials wrong?

Will I be equally puzzled if I try to take the AP Physics B exam?