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The rotational analog of force is called torque. It is given by
`tau` = radius × force
Although torque is a vector that lies in the axis of rotation, it is better understood in terms of the effect it has in rotating an object that is initially stationary. This expression of torque can be used to solve torque problems in rotational motion.
For example, imagine that you have a flat tyre and one of the nuts of the wheel is stuck tight. Suppose that your wrench is 0.3 m long. How much torque could you apply by stepping on the end of the wrench, if you weigh 115 pounds?
Now suppose that is not enough and you have a 0.6 m long hollow pipe that could be slipped over the wrench. What torque could you now apply?
Your mass = 115 lbs = `0.453592*115` kgs = 52.1631 kgs
Converting mass to force, your mass is then `52.1631*9.81` = 511.7198 N
The length of the wrench is 0.3 m.
Therefore torque applied initially, `tau_1 ` = `r_1F` = `0.3*511.7198` N-m
= 153.52 N-m.
After using the hollow pipe the radius of rotation increases to (0.3+0.6)=0.9 m, hence torque applied now,
`tau_2` = `r_2F` = 0.9*511.7198 N-m
= 460.55 N-m.
Thus, there will be a threefold increase of rotational force (torque) which will hopefully overcome the stuck nut’s rotational inertia.
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