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