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**preview**shows page 1. to view the full**4 pages of the document.**● 11-1 Torque

● The tendency for a force to cause a rotation increases with

the distance, r, from the axis of rotation to the force

● Torque: = rF; units: N*m; torque is the tangential force, F

is the magnitude of the applied force (only when applied on

tangential)

● The above equation is only for tangential forces

● If the force is applied in the radial direction along the axis of

rotation, the axle on which the object turns will produce an

equal and opposite force and it will remain at rest

● Radial force produces zero torque

● If the force is applied an angle to the radial line, first

resolve it into components; Fcos is the radial component

and therefore zero, Fsin is the tangential component

● General definition of Torque: = r(Fsin ); units: N*m

● The torque can also be defined as the cross product

between the radius and force vectors

● Moment arm: the perpendicular distance from the axis of

rotation to the line of the force (line draw through the force

vector) r = rsin

● The torque can also be written as the moment arm times the

force: = r F

● A torque applied to an object produces an angular

acceleration; if a torque acts on an object at rest it will start

rotating and if it acts on a rotating object it will change its

velocity

● Torque>0 if it causes counterclockwise angular acceleration;

T<0 if the torque causes a clockwise angular acceleration

● W/ more than one torque in a system, the sign of each is

determined by the angular acceleration it alone produces

● If the sum of 2+ torques is positive, acceleration is

counterclockwise; if negative clockwise

● 11-2 Torque and Angular Acceleration

● A single torque acting on an object causes it to have angular

acceleration

● = /I; = I

● Newton’s Second Law for Rotational Motion: = I

11-3 Zero Torque and Static Equilibrium

● Simply because the forces on an object sum to zero does not

guarantee the object remains at rest

● For an object to remain completely at rest (no translation or

rotation) two conditions are imposed

○The net force acting on the object must be zero so that

there is no translational acceleration

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