Why doesn't the gravity affect the torque along the z axis?

[Physicslearner1]

Homework Statement

Homework Equations

The Attempt at a Solution

I understand in general the argument of the problem, the only thing which I'm not sure of is why the gravity doesn't affect the torque. My guess is that it gets canceled by the normal force that is applied on the axle but I'm not 100 % sure.

Thanks ![/B]

 

[kuruman]

Can gravity exert a torque in the z-direction?

 

[Physicslearner1]

Can gravity exert a torque in the z-direction?

Why couldn't it ? Torque is defined as the cross product of the distance from the origin and the net force, right ?

 

[kuruman]

Torque is defined as the cross product of the distance from the origin and the net force, right ?

Almost. Distance is a scalar, not a vector. If force $\vec{F}$ is applied at position vector $\vec{r}$, the torque about the origin is $\vec{r} \times \vec{F}$.

What is the direction of the torque if the force is gravity?

 

[Physicslearner1]

Almost. Distance is a scalar, not a vector. If force $\vec{F}$ is applied at position vector $\vec{r}$, the torque about the origin is $\vec{r} \times \vec{F}$.

What is the direction of the torque if the force is gravity?

135 degrees in the xy plane ?

 

[kuruman]

The angle is unimportant. What matters is that the torque is in the xy plane. In what direction is the angular momentum of the wheel?

 

[haruspex]

Torque is defined as the cross product of the distance [correction by Kuruman: displacement] from the origin and the net force, right ?

And what is the angle between the vector product and each of the original vectors?

 

[Physicslearner1]

And what is the angle between the vector product and each of the original vectors?

It's perpendicular to both of them

 

[haruspex]

It's perpendicular to both of them

Right. And the force of gravity is in the z direction, so any torque it exerts must be at right angles to the z direction.

 

[Physicslearner1]

Right. And the force of gravity is in the z direction, so any torque it exerts must be at right angles to the z direction.

Ok, but I'm still not sure of understanding why torque is disregarded.

 

[kuruman]

In what direction is the torque?
In what direction is the angular momentum?
What is the direction in which the angular momentum can change?
How is the torque vector related to the change of angular momentum vector?

 

[haruspex]

Ok, but I'm still not sure of understanding why torque is disregarded.

For the moment, suppose the turntable is stationary. We drop a lump of putty on one edge. This exerts a torque about a horizontal axis. Will the turntable tip? Why not?