Homework Help: Does the torque increase or decrease as the angle increase?

1. Jul 7, 2010

mandy9008

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
A=Lsinө
τ=Amgsinө

3. 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

2. Jul 7, 2010

zhermes

Re: torque

What's the question here?

3. Jul 7, 2010

mandy9008

Re: torque

the answer in bold is incorrect

4. Jul 7, 2010

zhermes

Re: torque

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.