Rotational Kinematics/Dynamics

 

Rigid Body Kinematics

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.

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Rotational Inertia

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

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Rigid Body Dynamics

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.

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Rigid Body Dynamics Examples

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

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Work and Energy in Rotational Motion

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.

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Rolling of Rigid Bodies

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

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Rotational Kinematics

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

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Torque

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

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Pendulums and Rotational Energy

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

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Radial Acceleration

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.

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Experiment 4

Uniform circular motion experiment setup and procedure.

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Rotational Motion

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.

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Rotational Dynamics

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.

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

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Rotational Kinematics Review

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

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Rotational Dynamics Review

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.

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Rotational Dynamics and Energy

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

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Turntable

Frictional torque acting on a spinning uniform circular disc.

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Stall Torque of Motor

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

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Unrolling Spool of Wire

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

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Rigid Rotor

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

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Dropping Yo-Yo

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

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Glancing Collision

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

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Angular Acceleration

Motion of a hinged bar falling from rest.

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Gyroscope

Angular velocity and torques of a spinning gyroscope.

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Colliding Rotating Washers

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

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Sliding and Rolling Bowling Ball

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

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Falling Pulley

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

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Merry-Go-Round

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

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Torque and Moment of Inertia

Angular accelerations resulting from torques applied to two wheels.

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Rolling Without Slipping

Velocities of points on a rolling wheel.

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Torque, Rotation, and Translation

Rotational and translational motion of a descending yo-yo.

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Rolling Cylinder

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

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Angular Dynamics

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

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Elastic Collision

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

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Rolling Wheel

Translational and rotational kinematics and dynamics of a bicycle wheel.

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