http://www.ck12.org Chapter 8. Angular Motion and Statics
FIGURE 8.5
Once again,τ=r(Fsinθ), but this time sinceθ 6 = 90 ◦, the equation does not reduce toτ=rF.
Therefore,τ= ( 2. 20 m)( 95. 0 N)sin 130◦= 160. 1 m∗N
Check Your Understanding
- Why do we not calculate the torque using the cosine of the angle betweenrandF?
Answer:The cosine of the angle would give the component of force that acts to pull an object, not turn it. The
components ofFinFigure8.5 are drawn with red dashes. It should be clear that the perpendicular component
(Fy)is the component of force used for rotation. Hence,τ=r(Fsinθ)
- Mathematically, the definition of torque can also be expressed asτ= (rsinθ)F. In other words, we can always
assume thatF, rather than a component of the force, is responsible for rotation. How can this be?
Answer:It helps to look at what is often referred to as the line of action of the force. The line of action is represented
inFigure8.6 as the black dashed line that represents the direction in whichFacts.
We can see from the figure thatrsinθis the perpendicular distance to the line of action.Thus we can consider the
torque asτ= (rsinθ)F.