(Mechanics) Explain why... (1 Viewer)

[QZP]

Can someone explain why for (ii) its = -g sin? Not = g sin?

When you resolve the forces tangentially, I thought it'd just be = g sin.

The solution says "The negative sign is because the force is opposite to the direction of the increase of s" but this doesn't make sense to me. Explain please!

 

[Carrotsticks]

Think of simple harmonic motion. This equation is very similar to it (notice that the equation looks just like d/dx(1/2 v^2) ?

Imagine a particle in SHM moving away from the origin towards the positive extremity. The force is pulling the particle towards the centre of motion x=0, which is opposite to the direction that the particle is moving, so acceleration is negative.

Likewise for this expression.

 

[QZP]

Think of simple harmonic motion. This equation is very similar to it (notice that the equation looks just like d/dx(1/2 v^2) ?

Imagine a particle in SHM moving away from the origin towards the positive extremity. The force is pulling the particle towards the centre of motion x=0, which is opposite to the direction that the particle is moving, so acceleration is negative.

Likewise for this expression.

Right, thanks! I completely missed that the scenario was a pendulum.