What is the role of torque in rotational motion?

[eterna]

Homework Statement

http://postimg.org/image/mzdo4kp7b/

wouldn't the initial angular speed of 50rad/s cause some rotation about the axis at B (so shouldn't the FBD include a torque about B?)


http://postimg.org/image/nad9b9rqn/
And in this question, I don't know what Mz is. Is it due to the angular speed of 60000rpm?

Homework Equations

The Attempt at a Solution

 

[paisiello2]

1. An angular speed doesn't cause a rotation, it is a rotation- itself caused by a torque.

2. It looks like the 2nd sketch shows a FBD in plan. In that case Mz is the moment or torque caused by the inertia of the test tube contents. Again, an angular speed does not cause a torque but an angular acceleration does. What's missing is the reactions of the clamp that holds the test tube in place in the centrifuge.

 

[haruspex]

wouldn't the initial angular speed of 50rad/s cause some rotation about the axis at B (so shouldn't the FBD include a torque about B?)

It does create a torque on the wall+floor system. When allowed to touch the ground, it will cause a horizontal frictional force on the ground, towards the wall, and an equal and opposite horizontal force on the hinge at the wall. It cannot create a torque on itself.

http://postimg.org/image/nad9b9rqn/
And in this question, I don't know what Mz is. Is it due to the angular speed of 60000rpm?

As paisiello2 says, it's the torque required to achieve the angular acceleration the tube undergoes. You need to compute that acceleration.

What's missing is the reactions of the clamp that holds the test tube in place in the centrifuge.

I don't understand that comment. The question asks for net force and torque. It doesn't care how that is applied physically.

 

[paisiello2]

I was referring to the FBD. The value of Mz will depend on where the forces are applied.

 

[haruspex]

I was referring to the FBD. The value of Mz will depend on where the forces are applied.

No, it's the net torque required to make the test tube's angular velocity increase at a certain rate. It is independent of where the forces are applied. They might be large forces along lines that are close together, or smaller forces on lines that are further apart.

 

[paisiello2]

I understand what you are saying now. I was confused by a FBD that only showed the resultant forces. I usually expect to see all the forces acting on the body.