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.
• 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.
Moment of Inertia