Torque Web Quest

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Part I: Definition of TorquePart I: Definition of Torque

Torque is defined as the tendency to produce a change in rotational motion.

Torque is defined as the tendency to produce a change in rotational motion.

Examples:

Torque is Determined by Three Torque is Determined by Three Factors:Factors:

• The The magnitudemagnitude of the applied force. of the applied force.

• The The directiondirection of the applied force. of the applied force.

• The The locationlocation of the applied force. of the applied force.

• The The magnitudemagnitude of the applied force. of the applied force.

• The The directiondirection of the applied force. of the applied force.

• The The locationlocation of the applied force. of the applied force.

20 N

Magnitude of force

40 N

The 40-N force produces twice the torque as does the 20-N force.

Each of the 20-N forces has a different torque due to the direction of force. 20 N

Direction of Force

20 N

20 N20 N

Location of forceThe forces nearer the end of the wrench have greater torques.

20 N20 N

Units for TorqueUnits for Torque

Torque is proportional to the magnitude of F and to the distance r from the axis. Thus, a tentative formula might be:

Torque is proportional to the magnitude of F and to the distance r from the axis. Thus, a tentative formula might be:

= Fr = Fr Units: Nm or lbft

6 cm

40 N

= (40 N)(0.60 m) = 24.0 Nm, cw

= 24.0 Nm, cw = 24.0 Nm, cw

Sign Convention for Sign Convention for TorqueTorque

By convention, counterclockwise torques are positive and clockwise torques are negative.

Positive torque: Counter-clockwise, out of page

cw

ccw

Negative torque: clockwise, into page

Part II: Moments of InertiaPart II: Moments of Inertia• The moments of inertia for many shapes can The moments of inertia for many shapes can

found by using the following:found by using the following:

– Ring or hollow cylinder: Ring or hollow cylinder: II = = MRMR22

– Solid cylinder: Solid cylinder: II = (1/2)= (1/2) MRMR2 2 (use for part II in lab)(use for part II in lab)

– Hollow sphere: Hollow sphere: II = (2/3)= (2/3) MRMR22

– Solid sphere: Solid sphere: II = (2/5)= (2/5) MRMR22

Rotational InertiaRotational Inertia

• A rotating mass on a rod A rotating mass on a rod can be described with can be described with variables from linear or variables from linear or rotational motion.rotational motion.

Rotational InertiaRotational Inertia• To put the equation into rotational motion variables, the To put the equation into rotational motion variables, the forceforce is is

replaced by the replaced by the torquetorque about the center of rotation. about the center of rotation.

• The The linear accelerationlinear acceleration is replaced by the is replaced by the angular acceleration.angular acceleration.

Linear and Angular AccelerationLinear and Angular Acceleration

a = a rRadius of motion

(m)

Linear acceleration

(m/sec2)

Angular acceleration (kg)

Rotation and Newton's 2nd Rotation and Newton's 2nd LawLaw

• If you apply a torque to a wheel, it will spin in the direction of If you apply a torque to a wheel, it will spin in the direction of the torque. the torque.

• The greater the torque, the greater the angular acceleration.The greater the torque, the greater the angular acceleration.

Part III: Angular Part III: Angular MomentumMomentum

• Momentum Momentum resulting from an resulting from an object moving in object moving in linear motion is linear motion is called called linear linear momentummomentum. .

• Momentum Momentum resulting from the resulting from the rotation (or spin) of rotation (or spin) of an object is called an object is called angular momentumangular momentum..

Calculating angular Calculating angular momentummomentum

Angular momentum is calculated in a similar way to linear momentum, except the mass and velocity are replaced by the moment of inertia and angular velocity.

Angularvelocity

(rad/sec)

Angularmomentum(kg m/sec2)

L = I

Moment of inertia(kg m2)