Demonstration of failure of simple harmonic motion for ball in circular well; calculation of T does not agree with SHM.

Correspondence between rotational and linear motion; X->θ, v->ω, a->α, m->I.

Moments for disk, sphere, rod; parallel axis theorem; perpendicular axis theorem.

Conversion of linear KE to rotational KE; calculation of flywheel dimensions to store braking energy in car.

Conversion of rotational KE to linear KE from car flywheel; rotational KE of sun, earth and potential for use.

Decreasing period of Crab nebula; images of magnet flywheels, stroboscopic images of Crab, X-ray image from Chandra.

Calculation of acceleration based on Newton's second law.

Proof that acceleration is independent of M, R; a for various geometries, with demonstration.

Acceleration of rolling down slope calculated; analysis of friction force and minimum μ_s for rolling.

Explanation of longer than expected period for ball rolling on circular track in simple harmonic motion using rotational energy.

Summary of analogies between rotation and linear motion.

Rotation about a fixed axis; definitions of angular velocity and angular acceleration; Right-hand rule; rotational motion with constant angular acceleration; relationship between angular velocity, linear velocity, and acceleration, with example.

Definition of rotational kinetic energy, with example; definition of moment of inertia for a rigid body; moment of inertia example.

Torque and force; angular momentum and torque; torque and angular momentum of a conical pendulum; torque and angular acceleration; rigid body angular acceleration, with examples; torque due to gravity, with examples; conservation of angular momentum.

Rotational dynamics examples, including particle on a string and spinning bicycle wheel.

Work-energy theorem in rotational motion, with examples; angular impulse, with example; decomposition of displacement into translation and rotation; rolling motion of cylinders and spheres.

Rolling motion of a rigid body, such as a cylinder or a sphere, with several examples; angular momentum and collisions, with example; gyroscope precession.

Rotation about a fixed axis; definitions of angular velocity and angular acceleration; right-hand rule; rotational motion with constant angular acceleration; relationship between angular velocity, linear velocity, and acceleration, with example.

Definition of rotational kinetic energy, with example; definition of moment of inertia for a rigid body; table of rotational inertia values for various objects; moment of inertia example.

Torque and force; angular momentum and torque; torque and angular momentum of a conical pendulum; torque and angular acceleration; rigid body angular acceleration, with examples; torque due to gravity, with examples; conservation of angular momentum.

Rotational dynamics examples, including particle on a string and spinning bicycle wheel.

Work-energy theorem in rotational motion, with examples; angular impulse, with example; decomposition of displacement into translation and rotation; rolling motion of cylinders and spheres.

Rolling motion of a rigid body, such as a cylinder or a sphere, with several examples; angular momentum and collisions, with example; gyroscope precession.

Vector associated with angular motion (right-hand rule); angular velocity and angular acceleration defined; tangential and radial acceleration defined; rolling without slipping.

Torque defined; conditions for rotational static equilibrium; torque and rotational dynamics; moment of inertia; parallel axis theorem.

Simple and physical pendulums defined, with equations for period; parallel axis theorem defined; kinetic energy of rotational motion; summary of linear and rotational dynamics.

Radial acceleration defined; magnitude of radial acceleration, including alternate forms; direction of radial acceleration; cylindrical coordinate system; vectorial description of circular motion; circular motion example problem.

Uniform circular motion experiment setup and procedure.

Rotation and translation of a rigid body; translational motion of the center of mass; fixed axis rotation; angular and tangential velocity and acceleration; tangential force and torque; moment of inertia; parallel axis theorem; strategy for calculating moment of inertia.

Angular velocity and angular acceleration for fixed axis rotation; tangential velocity and tangential acceleration for fixed axis rotation; Newton's second law applied to rotating element; torque about a fixed axis; definition of moment of inertia; rotational work and rotational kinetic energy; rotational work-kinetic energy theorem; definition of rotational power.

Fixed axis rotational kinematics, with definitions of angular velocity, angular acceleration, tangential velocity, tangential acceleration, and radial acceleration.

Torque, rotational kinetic energy, moment of inertia, and rotational work defined; strategy for computing moment of inertia; translational and rotational kinematics/dynamics combined; kepler's Law for conservation of angular momentum.

Angular acceleration as a function of moment of inertia; motion of a rolling wheel.

Motion of a wheel rolling down an incline; potential and kinetic energy of various objects sliding or rolling down an incline.

Frictional torque acting on a spinning uniform circular disc.

Solution (PDF)

Calculating the stall torque and torque at maximum power of a motor.

Solution (PDF)^#

A rod is hit off-center; finding velocity, ω, position, and kinetic energy.

Solution (PDF)^#

A string wrapped around the inner part of a yo-yo is pulled; find direction of rolling.

Solution (PDF)^#

A spinning disk is pushed against a stationary one; decide on conservation of L, kinetic energy; find ω.

Solution (PDF)^#

Two blocks connected over pulley, on separate slopes; find α of pulley, a, and T.

Solution (PDF)^#

Explaining transition from skidding to rolling of plane wheels on touchdown.

Solution (PDF)^#

5-part problem; finding moment of inertia, frictional force, acceleration, angular acceleration, and kinetic energy.

Solution (PDF)^#

4-part problem; finding center of mass, moment of inertia of rotor; α from gravity and ω at vertical.

Solution (PDF)^#

Acceleration, angular acceleration, and tension in string of yo-yo.

Solution (PDF)^#

Straight rod brushes against fixed object; finding ω, kinetic energy, speeds of both ends after collision.

Solution (PDF)^#

Motion of a hinged bar falling from rest.

Solution (PDF)

Angular velocity and torques of a spinning gyroscope.

Solution (PDF)

Angular velocity and torques of a spinning gyroscope.

Solution (PDF)

5-part problem; initial L and kinetic energy of washer, frictional torque, final ω of washers, average τ in collision.

Solution (PDF)^#

Calculating ω and kinetic energy for bowling ball when it begins to roll; loss of KE.

Solution (PDF)^#

6-part problem; for pulley connected to ceiling by string, finding equations of motion, a, falling time, and tension.

Solution (PDF)^#

6-part problem; calculating α, ω, power exerted on merry-go-round; ω and kinetic energy after I changes.

Solution (PDF)^#

Angular accelerations resulting from torques applied to two wheels.

Solution (PDF)^#

Velocities of points on a rolling wheel.

Solution (PDF)^#

Rotational and translational motion of a descending yo-yo.

Solution (PDF)^#

Rotational and translational motion of a solid cylinder thrown along a wooden floor.

Solution (PDF)^#

Motion of a rotating merry-go-round, before and after children move to the center.

Solution (PDF - 2.0 MB)^#

Elastic collision between two carts and motion of a cart up an inclined plane.

Solution (PDF - 1.1 MB)^#

Translational and rotational kinematics and dynamics of a bicycle wheel.

Solution (PDF - 1.1 MB)^#

4-part friction and rotational kinematics problem; drawing a free-body diagram, calculating tensions, and finding unknown mass.

Solution (PDF)^#

5-part rotational dynamics problem; finding τ, I, equation of motion, T, and force at pin.

Solution (PDF)^#

5-part rotational dynamics problem; apple revolves on a string at an angle to the horizontal; finding v, a_c, ω, α.

Solution (PDF)^#

Finding acceleration of bowling ball rolling in accelerating subway car.

Solution (PDF)^#