*door top view F1F2

axis of rotation r1

r2

Where:F = forcer = lever arm= perpendicular distance from the axis of rotation to the line along which the forces acts.here.,α∝ F

*door top view F1F2

axis of rotation r1

r2

α ∝ F x r Moment of Force or Torque (τ)

α ∝ τ

a vector quantity that determines the ability of a force to introduce rotation. τ = rF ; unit: mN

1.Magnitude of the applied force2.Distance from point of application to

pivot (location of applied force)3.Angle ( direction of the applied force)

F1

F2

F3

r1

r2

τ F1 > τ F2

τ F2 < τ F1

τ = 0

NOTE: in general τ = r⊥F

Remind us that we must use the distance from

the axis of rotation that is perpendicular to the

line of action of the force

r⊥ = r sin ⴱ

F2

ⴱτ = rF⊥l = rF⊥ sinⴱ

We can use τ = r⊥ F or τ = r F⊥ or τ = r F sin ⴱ to calculate the torque whichever is easiest.Line of action of a force - the line of motion of a force is an imaginary line of indefinite length drawn a long the direction of the forceThe moment arm is the perpendicular distance from the line of action of a force to the axis of rotation.

1. An 80 N acts at the end of a 12 cm wrench as shown. Find the torque.

80 N12 cm ⴱ =60o

2. Find the resultant torque about axis A for the arrangement shown:

ⴱ =30o ⴱ =30o 4 m

2 m6 m

F3 = 20 N

F2 = 40N

F1 = 30 N

Torque is a vector quantity that has a direction as well as magnitude

Thumb F (force)Pointer r (moment arm)Middle finger direction of τ (torque)

↑ Up +↓ Down -

→ Right +← left -⊙ Outward +⊗ Inward -CC Counterclockwise +C clockwise -

→ ⊗ ↑

← ⊙⊙ →

↑

↑

Car at rest Constant speed, no change in direction

An object is said to be in equilibrium if it does not have linear acceleration and angular acceleration

Linear acceleration is Zero if….

Angular acceleration is Zero if….

wheel at rest Constant rotation

The center of mass lies at the geometric center for a

symmetric, uniform density object.

h/3

hR

h/2

h

h/2

h

The center of mass can be outside the mass of the body.

Center of mass

Ability of an object to return to its original position after it is displaced or tilted slightly

- CG is below of point of support- the objects return to its original position

- When object is displaced, the object moves even farther from its position

- When object is displaced, the object remain in its position

cm