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.
• What causes the centripetal force in the first place?
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
• 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
Torque
• Depending on where the force is applied, torque will increase or decrease.
• Torque is a vector
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
• 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 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).
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
• 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 mass
• Depending on if the object is symmetrical or not, the center of mass is either easy or hard to find.
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
• 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 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.