2. Torque Web Quest Helpful Hints

3. Part I: Definition of Torque Torque is defined as the tendency to produce a change in rotational motion. Examples:

4. Torque is Determined by Three Factors: The magnitude of the applied force.The magnitude of the applied force. The direction of the applied force.The direction of the applied force. The location of the applied force.The location of the applied force. The magnitude of the applied force.The magnitude of the applied force. The direction of the applied force.The direction of the applied force. The location of the applied force.The location 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   Location of force The forces nearer the end of the wrench have greater torques. 20 N

5. Units for Torque Torque is proportional to the magnitude of F and to the distance r from the axis. Thus, a tentative formula might be:  = Fr Units: N  m or lb  ft 6 cm 40 N  = (40 N)(0.60 m) = 24.0 N  m, cw  = 24.0 N  m, cw

6. Sign Convention for Torque 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

7. Part II: Moments of Inertia The moments of inertia for many shapes can found by using the following:The moments of inertia for many shapes can found by using the following: –Ring or hollow cylinder: I = MR 2 –Solid cylinder: I = (1/2) MR 2 (use for part II in lab) –Hollow sphere: I = (2/3) MR 2 –Solid sphere: I = (2/5) MR 2

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

9. Rotational Inertia To put the equation into rotational motion variables, the force is replaced by the torque about the center of rotation.To put the equation into rotational motion variables, the force is replaced by the torque about the center of rotation. The linear acceleration is replaced by the angular acceleration.The linear acceleration is replaced by the angular acceleration.

10. Linear and Angular Acceleration a = a r Radius of motion (m) Linear acceleration (m/sec 2 ) Angular acceleration (kg)

11. Rotation and Newton's 2nd Law If you apply a torque to a wheel, it will spin in the direction of the torque. The greater the torque, the greater the angular acceleration.

12. Part III: Angular Momentum Momentum resulting from an object moving in linear motion is called linear momentum.Momentum resulting from an object moving in linear motion is called linear momentum. Momentum resulting from the rotation (or spin) of an object is called angular momentum.Momentum resulting from the rotation (or spin) of an object is called angular momentum.

13. Calculating angular momentum 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. Angular velocity (rad/sec) Angular momentum (kg m/sec 2 ) L = I  Moment of inertia (kg m 2 )