Rotational dynamics
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Rotational dynamics. Chapter 8. Masses. Up ‘til now, we have assumed that all masses are essentially points in space. From this point onwards, we will treat all objects as extended . Rotation. We established earlier that centripetal force causes circular motion.

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Masses
Masses

  • Up ‘til now, we have assumed that all masses are essentially points in space.

  • From this point onwards, we will treat all objects as extended.


Rotation
Rotation

  • We established earlier that centripetal force causes circular motion.

  • What causes the centripetal force in the first place?


Rotation1
Rotation

  • Remember, for all objects, we are assuming that the object rotates around a fixed axis.

  • Objects rotating around this axis feel the centripetal force.


Torque
Torque

  • The ability of a force to rotate an object around that axis is measured by a quantity known as torque.

  • Torque is dependent on three things

    • Force

    • Lever arm

    • The angle between the two


Torque1
Torque

  • Depending on where the force is applied, torque will increase or decrease.

  • Torque is a vector


Sample problem
Sample problem

  • A mechanic applies a force of 400 N at an angle of 20 degrees on this wrench. The wrench is 0.3 meters long. What is the torque?


Net torque
Net Torque

  • Like force, there can be multiple torques on an object.

  • You can add those all up to find the net, or total, torque.

    • ∑τ=τ1+τ2+τ3+…

    • Keep in mind each torque can be positive or negative, so the net torque will be + or –.


Sample problem1
Sample problem

Find the net torque of all the forces on the triangle around the fixed point. (ignore the d’s and f’s in the diagram).


Rotation2
Rotation

  • The axis of rotation is easy to find for some objects. Doors, the windows in the back, all have hinges.

  • What if something is flying through the air?


Center of mass
Center of Mass

  • If gravity is the only force acting on something, that object will rotate about its center of mass.

  • This in turn means that airborne objects undergo both linear and rotational motion


Center of mass1
Center of mass

  • Depending on if the object is symmetrical or not, the center of mass is either easy or hard to find.


Center of mass2
Center of Mass

  • It’s easier to rotate some objects around a certain axis than others.

    • What’s the best way to swing a bat?


Moment of inertia
Moment of Inertia

  • An object’s ability to resist rotational motion is measured by its moment of inertia.

  • Mass and moment of inertia both resist motion

    • Mass resists linear

    • M.o.I resists rotational


Moment of inertia1
Moment of Inertia

  • How an object is shaped determines its moment of inertia.

    • The further the mass is from the axis, the greater the m.o.i.



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