A student plots torque τ versus angle θ for a wrench as the angle increases from 0rad. The graph is nearly linear for small angles before curving upward toward a maximum. Which of the following best explains why the initial portion of the graph is almost a straight line?
a) Because as the wrench first begins to turn, the person typically pushes harder, and with τ=rF this makes τ grow almost proportionally with θ.
b) Because for small angles sinθ≈θ, so τ=rFsinθ increases nearly linearly with θ.
c) Because at small angles cosθ≈1, so the lever arm is essentially constant and any rise in force makes τ appear to vary linearly with θ.
d) Because torque equals Iα, and for small rotations the angular acceleration is nearly constant, resulting in τ increasing roughly linearly with the angle turned.