# Torque

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*Helena Dedic*

*If you need to understand the concept of center of mass, please see the link below:*

CENTER OF MASS

- A force causes a free object to move in a translational motion if it is applied at the centre of mass of the object or the line of force passes through the centre of mass.

- When a force is not applied at the centre of mass of a free object or when the line of force does not pass through the centre of mass then it causes this object to move in a complex way that involves both translation (i.e.: movement of the center of mass) as well as rotation (i.e.: movement around the center of mass.)

__OBSERVATIONS OF AN OBJECT:__

a)When a force acts at the pivot or when a line of force passes through the pivot,

the object does not begin to rotate.

b)When a force acts at some distance from the pivot, the object begins to rotate.

- Lever arm is a vector that points from the pivot to the point where the force acts.

**TORQUE**:**A cause of a change of the angular velocity**(e.g.: a rotating wheel stops or it begins to rotate faster.

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The symbol for torque is .
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The magnitude of the torque depends on the magnitude of the lever arm, the magnitude of the force and the angle between these two vectors:**Magnitude and direction of the torque**:

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In special cases where the axis of rotation is given: The torque is **positive** when the torque causes the object to rotate in the **counter-clockwise** direction and **negative** when the torque causes the object to rotate in the **clockwise** direction.

- In general the torque is a
__vector product__of the lever arm and the force:

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### Static Equilibrium Revisited

- An object is in static equilibrium
**if and only if**and , where the net torque is the sum of all torques and the net force is the sum of all forces acting on an object. - Static equilibrium
**problem solving strategy**:

- Determine all forces acting on an object and draw an arrow for each force indicating:
- A point where this force is applied
- In which direction this force acts

- For each force:
- Identify the magnitude and the direction of lever arm
- Draw a diagram consisting of lever arm and force vectors and determine the angle between these two vectors
- Determine the direction of the torque and then compute its magnitude.

- Substitute into the equation
- Select the coordinate system
- Draw a free-body diagram
- Compute the components of the forces
- Substitute into the equations and
- Solve the system of three equations using the method of substitution