Does the torque increase or decrease as the angle increase?

[mandy9008]

Homework Statement

A simple pendulum consists of a small object of mass 2.4 kg hanging at the end of a 2.0 m long light string that is connected to a pivot point.
(a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 3.0° angle with the vertical.
(b) Does the torque increase or decrease as the angle increase?
(c)Explain your answer.

Homework Equations

A=Lsinө
τ=Amgsinө

The Attempt at a Solution

a. A=2.0m sin 3.0
A= 0.105m

τ=0.105m (2.4kg)(9.8m/s²)sin 3.0
τ= 0.129 Nm

b. angle will increase
c. Since angle increases, sin of the angle also increases

 

[zhermes]

What's the question here?

 

[mandy9008]

the answer in bold is incorrect

 

[zhermes]

You have an extra sin in there.
You're correct that the equation for torque is
$$\tau = \vec{r} \times \vec{F} = mgl sin\theta$$
So it's based on the cross product of the displacement vector 'r' (the vector from the pivot point to the mass) and the force vector 'F' (which is the force due to gravity). The angle between those vectors is theta.
But you need to use 'l' as the full length, and the sin of theta takes into account the angle.

 

[rwisz]

. As torque is directly proportional to the sin of the angle, it will also increase. This is because the perpendicular distance from the pivot point to the force of gravity increases, resulting in a larger lever arm and therefore a larger torque.