This page organizes the solved example problems involving rotation into several common categories. Most problems appear in more than one category. An alphabetical list of rotation problems is shown in the table of contents in the left navigation bar.
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Finding Moment of Inertia
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Moment of Inertia of a Solid Sphere — Integrate to find the moment of inertia of a solid sphere.
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Moment of Inertia of a Block — Evaluate the integral to find the moment of inertia of a rectangular block.
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Ballistic Pendulum Revisited — A version of the ballistic pendulum problem in which rotational effects are important.
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Not-So-Simple Pendulum — Compares the simple pendulum model with a slightly more detailed one.
Rotational Version of Newton's 2nd Law
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Big Ben — Check Parliament's math by calculating the period of Big Ben's pendulum.
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Spinning Top — The rapidly spinning Symmetric Top exhibiting Precession under the force of gravity (near-earth) is a classic Physics problem.
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Accelerating Flywheel — Acceleration of a symmetric object about a fixed axis under constant torque (single-axis).
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The Ladder Problem — A standard statics problem.
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Rolling Coin — A Coin rolling on its edge with a slight tilt will trace out a circle. What is its radius?
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Sliding Yardstick — What happens to a yardstick (or meter stick) supported by two fingers as those fingers are slowly moved toward each other?
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Locking Your Bike — Determine how the weight of a bicycle plus rider is divided between the wheels in various circumstances.
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Down the Alley — Determine the final speed of a ball that is initially sliding without rotation.
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Down the Ramp — Find the acceleration of a ball rolling without slipping on an inclined plane.
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Not-So-Simple Pendulum — Compares the simple pendulum model with a slightly more detailed one.
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Down the Well — A mass falling while attached to a massive pulley.
Rotational Energy
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Rotating a Space Ship — Changes in Angular Velocity when the Moment of Inertia is changed, but no torque applied.
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Twirling Skater — Changes in Angular Velocity when the Moment of Inertia is changed, but no torque applied.
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Pull Harder! — Examine the work needed to change the radius of rotation of an object rotating in a circle.
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Down the Alley — Determine the final speed of a ball that is initially sliding without rotation.
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Down the Ramp — Find the acceleration of a ball rolling without slipping on an inclined plane.
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Down the Well — A mass falling while attached to a massive pulley.
Angular Momentum and Torque
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Spinning Top — The rapidly spinning Symmetric Top exhibiting Precession under the force of gravity (near-earth) is a classic Physics problem.
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Rolling Coin — A Coin rolling on its edge with a slight tilt will trace out a circle. What is its radius?
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Down the Ramp — Find the acceleration of a ball rolling without slipping on an inclined plane.
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Not-So-Simple Pendulum — Compares the simple pendulum model with a slightly more detailed one.
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Down the Well — A mass falling while attached to a massive pulley.
Constant Angular Momentum
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Lost in Space — The dangers of angular momentum in outer space.
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A ball hits a bar and sticks to it. — find the angular velocity and the velocity of the final object's (bar + ball) center of mass
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Rotating a Space Ship — Changes in Angular Velocity when the Moment of Inertia is changed, but no torque applied.
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Twirling Skater — Changes in Angular Velocity when the Moment of Inertia is changed, but no torque applied.
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Pull Harder! — Examine the work needed to change the radius of rotation of an object rotating in a circle.
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Ballistic Pendulum Revisited — A version of the ballistic pendulum problem in which rotational effects are important.
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Down the Alley — Determine the final speed of a ball that is initially sliding without rotation.
Rolling Without Slipping
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Down the Alley — Determine the final speed of a ball that is initially sliding without rotation.
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Down the Ramp — Find the acceleration of a ball rolling without slipping on an inclined plane.
Statics
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The Ladder Problem — A standard statics problem.
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Sliding Yardstick — What happens to a yardstick (or meter stick) supported by two fingers as those fingers are slowly moved toward each other?
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Locking Your Bike — Determine how the weight of a bicycle plus rider is divided between the wheels in various circumstances.