Why is the moment arm length positive when I get negative?

[negation]

Homework Statement

a) What is the length, rmr_m, of the moment arm of the force F→F_vec about point p?

b) Find the torque τtau about p due to F→F_vec. Your answer should correctly express both the magnitude and sign of τ.

The Attempt at a Solution

a) I'm inclined to state the answer as -rsinΘ but apparently the answer is r sin Θ.
Is there a reason why the sign is positive?

 

[PhanthomJay]

Homework Statement

View attachment 68238

a) What is the length, rmr_m, of the moment arm of the force F→F_vec about point p?

b) Find the torque τtau about p due to F→F_vec. Your answer should correctly express both the magnitude and sign of τ.

The Attempt at a Solution

a) I'm inclined to state the answer as -rsinΘ but apparently the answer is r sin Θ.
Is there a reason why the sign is positive?

always use the magnitude ( positive number) of the force and position vectors and moment arm when calculating torques. The sign of the torque is then determined by clockwise or counterclockwise torque , ccw is plus in this example, cw is minus, simply by convention.

 

[negation]

always use the magnitude ( positive number) of the force and position vectors and moment arm when calculating torques. The sign of the torque is then determined by clockwise or counterclockwise torque , ccw is plus in this example, cw is minus, simply by convention.

Understood.

What about (b)? I'm really quite unclear about what moment of arm is and how it relates to torque. Would you mind shedding some light? (I appreciate)

 

[PhanthomJay]

Understood.

What about (b)? I'm really quite unclear about what moment of arm is and how it relates to torque. Would you mind shedding some light? (I appreciate)

There are several ways to calculate torque about a point. One such way is to use torque = magnitude of force times the perpendicular distance from the line of action of the force to point, where the perpendicular distance is called the 'moment arm'. Another is to use the cross product rule. Sign of torque is plus if ccw, minus if cw, using the convention that ccw torques are positive.

 

[negation]

There are several ways to calculate torque about a point. One such way is to use torque = magnitude of force times the perpendicular distance from the line of action of the force to point, where the perpendicular distance is called the 'moment arm'. Another is to use the cross product rule. Sign of torque is plus if ccw, minus if cw, using the convention that ccw torques are positive.

And the dashed lines extending from F vector is the moment arm?

 

[PhanthomJay]

And the dashed lines extending from F vector is the moment arm?

No, the moment arm is the perpendicular distance from the line of action of the force vector to the point, which woukld be r_m on your sketch.