Prove that dL/dt = r × F; angular momentum conserved when τ = 0; Spin angular momentum defined.

Critical angle calculated for ladder resting against a wall, based on μ.

Ladder stability as person walks from base to center of mass and further; overcoming maximal friction.

Demonstration of weight placed on ladder near critical angle at various positions.

Statics of a hanging object; position of center of mass for equilibrium; stability of several small objects.

Stability of rope walker with objects suspended to lower center of mass; demonstration of rope walker on zip line.

Calculation of acceleration for two blocks suspended over pulley with friction from masses and moment of inertia.

Summary of analogies between rotation and linear motion.

Relationship between forces and angular momentum; definition of the law of conservation of angular momentum; definition of torque; angular momentum and central forces, with examples.

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.

Conditions of equilibrium for particles and rigid bodies; torque axis; center of gravity; center of mass demonstration; stable and unstable equilibrium; coupled forces; equilibrium problem-solving strategy with several examples.

Relationship between forces and angular momentum; definition of the law of conservation of angular momentum; definition of torque; angular momentum and central forces, with examples.

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.

Conditions of equilibrium for particles and rigid bodies; torque axis; center of gravity; center of mass demonstration; stable and unstable equilibrium; coupled forces; equilibrium problem-solving strategy with several examples.

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

Checklist for solving torque problems; angular momentum defined, with equation; angular impulse defined, with equation.

Rigid bodies; center of mass; pivoted lever; lever law; pivoted lever example problem; generalized lever law; definition of torque; torque sign convention; two geometric interpretations of torque; static equilibrium.

Definition of torque, including magnitude, direction, and sign convention; moment arm of a force; torque from tangential force; static equilibrium.

Static equilibrium involving torques.

Finding the cross product of two vectors.

Effectiveness of various methods of applying a force to a wrench to loosen a nut.

Forces acting on a uniform ladder leaning against a wall.

Torque applied to a stuck door by hand and by using a rope.

Finding the weight of a measuring stick in order to balance a suspended rock.

Position of the center-of-mass of a box on an inclined plane as it relates to the box tipping over.

Torque acting on an ankle.

Torque acting on a hip joint.

2-part problem; calculating force required and optimal angle for applying force.

Solution (PDF)^#

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

Solution (PDF)^#

Forces and torques acting on a runner rounding a circular track.

Solution (PDF)

Forces and torques acting on a person doing a pushup.

Solution (PDF)

Forces and torques acting on a plank holding a mass of bricks and supported by cables.

Solution (PDF)

Forces and torques acting on a plank leaning against a wall.

Solution (PDF)

Two masses connected by a rope wrapped around a pulley.

Solution (PDF - 2.0 MB)

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

Solution (PDF)