Definition and equations for T, v, ω, and centripetal acceleration, with example.

Causes of centripetal acceleration, and demonstration of straight path motion after loss of centripetal force.

Uniform circular motion calculations for planets, and graph showing that a_c, and thus gravity, falls off as 1/R².

Reasoning showing why centrifuges work, with demonstration.

Perceived gravity defined; examples in several positions including spinning; example of artificial gravity in a spinning space station.

Explanation of how small particles sink to side in a centrifuge; demo of centrifuging AgCl.

Demonstration of water in a spinning bucket feeling artificial gravity upwards.

Statement of Newton's first law; definition of inertial reference frame; calculation of a_c for Earth's rotation.

Period, frequency, angular velocity, linear speed, centripetal acceleration defined, with example.

Example of ball in rollercoaster; proof that h ≥ 2.5R for ball to make it around.

Dynamics of uniform circular motion; motion in a vertical circle, with example; conical pendulum, with examples.

Parallel-axis theorem, with example; perpendicular-axis theorem, with examples; definition of angular momentum of a particle; definition of central forces; angular momentum of a particle moving in a straight line; angular momentum of a particle in uniform circular motion; angular momentum of a conical pendulum.

Uniform circular motion; centripetal acceleration; non-uniform circular motion; reference frames; relativity of motion; problem-solving strategy for relative velocities with examples.

Dynamics of uniform circular motion; motion in a vertical circle, with example; conical pendulum, with examples.

Parallel-axis theorem, with example; perpendicular-axis theorem, with examples; definition of angular momentum of a particle; definition of central forces; angular momentum of a particle moving in a straight line; angular momentum of a particle in uniform circular motion; angular momentum of a conical pendulum.

Uniform circular motion; centripetal acceleration; non-uniform circular motion; reference frames; relativity of motion; problem-solving strategy for relative velocities with examples.

Projectile motion equations; circular motion equations; centripetal acceleration, with equation; imensional analysis method.

Position and displacement of object in circular orbit; magnitude of displacement; magnitude of velocity and angular velocity; direction of velocity; tangential acceleration defined; uniform circular motion; period and frequency of orbit.

Summary of circular motion, with equations; circular motion vector description, with equations; circular motion modeling problems; analysis of acceleration in circular motion.

Position vector of circular orbit; angular velocity and tangential velocity; radial acceleration; uniform circular motion; non-uniform circular motion; comparison of linear and circular motion at constant acceleration; problem solving strategy involving circular motion.

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

3-part problem; calculating tension in wire, critical angle, and safe speed for flight.

Solution (PDF)

3-part problem; finding normal force from wire and height the bead attains on the way back up.

Solution (PDF)^#

Speed and acceleration of an object moving in a circle of constant radius.

Forces and acceleration of objects moving in vertical circular paths.

Relative angular speed of two objects at different points on a merry-go-round.

Forces acting on two bodies rotating around a shaft with constant angular velocity.

Solution (PDF)

Motion of an object in a circular orbit along the inside of a cone.

Solution (PDF)

Finding velocity needed to keep a car from slipping on a banked turn.

Solution (PDF)

Motion of a plane tethered to a fixed point.

Solution (PDF)^#

Motion of an object along a frictionless loop-the-loop track.

Solution (PDF)

Forces acting on a suspended ring with sliding beads.

Solution (PDF)^#

Angular velocity of two bugs on a merry-go-round.

Linear acceleration of a bug on a merry-go-round.

Tangential acceleration of a bug on a merry-go-round.

Motion of a ball thrown from a merry-go-round.

Minimum angular speed required for "barrel of fun."

Speed of an object moving in a circular path with non-uniform acceleration.

Direction of acceleration vector for object in circular motion with increasing speed.

Forces acting on a passenger in a car navigating a circular turn.

Forces capable of producing centripetal acceleration.

Source of centripetal force for a ball moving on turning truck bed.

Determining spinning motion of a wrecked car.

Acceleration of ice sliding in a bowl.

Tension of a string holding a stone moving in a vertical circular path.

Acceleration of a puck moving in a uniform circle on a table.

Acceleration of a puck moving in a uniform circle on a table with a shorter lever arm.

Tension in a string holding a ball being swung in a vertical circle.

Speed of a point on the outside of a tire in relation to the speed of the center of mass.

Relative speeds of points on the outside of a rolling tire.

Direction of motion of points on the outside of a rolling tire.

Forces acting on a cube lying on a spinning turntable.

Tension in strings suspending a ball from a spinning vertical rod.

Work done on a ball rolling in a spiral path along the inside of a hollow cylinder.

Finding the spring constant of a spring; finding the radius of an object in uniform circular motion.

Solution (PDF)

Velocity and centripetal acceleration of a person on the Earth's surface.

Solution (PDF)

Motion of a car traversing a banked circular turn.

Solution (PDF)

Motion of a ball suspended from a string and travelling in a vertical circle.

Solution (PDF)

Finding maximum rotation period for planet from density; calculating periods.

Solution (PDF)

Maximum speed before skidding for car on frictional track for two different masses; Angular velocity.

Solution (PDF)^#

Period of a rotating disc attached to a spring.

Solution (PDF)

Motion of a car driving along the inside of a hollow cone.

Solution (PDF)

Dynamics of a system of a mass suspended from a vertical spinning rod by a string and pulley.

Solution (PDF)

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

Solution (PDF)

4-part problem; drawing free-body diagram and finding v, T for object; maximum speed with friction.

Solution (PDF)

Finding ω, T, f for nut revolving around axis on end of a rubber band.

Solution (PDF)

Speed and tension at the top of the circle for ball swinging around.

Solution (PDF)^#

4-part problem; finding compression necessary to launch pen into orbit; speed and radius in orbit.

Solution (PDF)

Motion of a water bucket spun in a vertical circle.

Solution (PDF)

Centripetal acceleration of a puck moving in a circle.

Solution (PDF)^#

Speed of an object with a constantly changing velocity vector.

Solution (PDF)^#

Kinematics and dynamics of a tethered ball traveling in a vertical circle.

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)