Torque & Rotational Statics

 

Conservation of Angular Momentum

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.

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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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Forces in Equilibrium

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.

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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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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.

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Angular Momentum

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

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Statics and Torque Review

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

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Rotational Statics

Static equilibrium involving torques.

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Cross Product

Finding the cross product of two vectors.

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Wrench and Nut

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

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Leaning Ladder

Forces acting on a uniform ladder leaning against a wall.

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Opening a Door

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

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Balanced Rock

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

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Center-of-Mass

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

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Equilibrium in an Ankle

Torque acting on an ankle.

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Equilibrium in a Hip

Torque acting on a hip joint.

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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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Equilibrium of a Runner

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

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Equilibrium of a Pushup

Forces and torques acting on a person doing a pushup.

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Static Equilibrium

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

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

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Torque and Angular Acceleration

Two masses connected by a rope wrapped around a pulley.

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