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Rotational Dynamics

  • D1-40: CENTRIPETAL FORCE ON ROTATING RUBBER BAND

    D1-40
    Demonstrate centripetal force and centrifugal reaction.
    A rubber band is stretched around a disc which can be rapidly rotated. Use stroboscope to stop the motion, showing that the rubber band stretches when the disc is rotated. The stretch becomes greater as the angular velocity is increased.
    D1, N2, LS1

  • D1-41 ROTATING WATER BUCKET

    D1-41
    Demonstrates centripetal force and centrifugal reaction
    Put some water in the bucket and rotate the bucket in a vertical circle over your head. The centripetal force provided by your arm keeps the water bucket moving in a circle, while the centrifugal reaction keeps the water in the bottom of the bucket, as long as the rotational velocity is sufficient.
    D1

  • D1-42: ROTATING WATER BUCKET WITH SPONGE

    D1-42
    Illustrate centripetal force and centrifugal reaction with a trick.
    Pour water into the can, then rotate the can over your head in vertical circles. Rotate the can more and more slowly as you move toward the class, so that the can stops upside down over some student's head. Then remove the sponge and squeeze the water back into the can.

  • D1-43: INERTIAL FORCES - BALLS IN ROTATING JARS

    D1-43
    Demonstrate inertial forces in bodies submerged in air and in water.
    On one side of the arm a ping-pong ball is suspended by a string from the top of a jar filled with air. On the opposite side of the arm a ping-pong ball is attached by a string to the bottom of a jar filled with water. When the arm is rotated, the ball in the air jar moves outward and the ball in the water jar moves inward.
    D1

  • D1-44: ACCELEROMETERS AND FRAMES OF REFERENCE

    D1-44
    Demonstrate the direction of the acceleration in both rotational and translational coordinate systems
    In each experiment the ping-pong balls act as accelerometers. When the jars are rotated, the ball suspended from the bottom of the water-filled jar moves toward the direction of the acceleration, while the ball suspended from the top of the air-filled jar moves in the direction opposite the acceleration. The ping-pong ball in the water-filled tube indicates the direction of the acceleration when the tube is accelerated linearly or rotated.

  • D1-51 BANKED CURVE MODEL

    D1-51
    Aid in explaining banked turns
    The model of the curved road is banked such that at the suggested maximum rate of speed the horizontal component of the normal force provides the centripetal force required to keep the car moving in its circular path, independent of the friction of the car wheels with the road.
    D1

  • D1-52: FAIRGROUND ROTOR

    D1-52
    Illustrate the application of rotational forces
    Place the little people onto their platform against the wall of the rotor and start the rotor in motion. A trip switch (just to the left of the peole in the close-up photo) removes the floor, but the people remain pinned against the wall due to centrifugal reaction, and do not fall due to friction with the wall of the rotor. When the rotor slows down, the frictional force of the people against the wall becomes less than component of the gravitational force down the wall and the people fall off the rotor. The entire assembly may be tilted while the rotor is in motion without causing the people to fall off.
    OS1

  • D1-53 LOOP-THE-LOOP

    D1-53
    Demonstrates centripetal force and conservation of energy in a rotating object

    This track can be described as three segments: the long upright segment, the loop, and the shorter upright segment. If you begin by placing the ball on the long upright segment at a height equal to the height of the loop (2R), the ball will roll down the track, begin to climb the loop, and then fall off and roll away. You can then repeat this at increasingly higher positions until the ball makes it all the way around the loop and begins to climb the shorter upright segment. In either case, be ready to catch it as it falls off afterwards!

    This is a good demonstration to encourage students to make predictions about its behaviour. Invite students to make arguments about what starting height will allow the ball to complete the full loop. A meter stick can be additionally provided upon request to aid in measuring the height.

    Background
    Motion of the ball down the track and around the loop-the-loop can be described in terms of gravitational potential energy, rotational and translational kinetic energy, and centripetal force. A ball of mass m and radius r must be released at some minimum height h above the bottom point of the track so that it will not leave the track while passing around the loop-the-loop.

    In order to stay on the track at the top of the loop the centrifugal reaction of the ball on the track must be equal to or greater than the gravitational force on the ball: mv^2/R = mg, or v^2 = gR, where v is its linear velocity at the top of the loop, R is the radius of the loop, and g is the acceleration of gravity. Conservation of energy dictates that at the top of the loop Iw^2/2 + mv^2/2 +2mgR = mgh, where the moment of inertia of the ball I = 2mr^2/5 and w is the angular velocity of the ball at the top of the loop.

    From these considerations we obtain the minimum starting height for the ball above the bottom of the loop-the-loop in order that the ball remain in contact with the track at all times: h = 2.7 R. In the case of an object sliding along a frictionless loop-the-loop, the height would be h = 2.5 R. Marks have been made at the points 2.5 R and 2.7 R. The ball remains in contact with the track at the top of the loop only when the height 2.7 R is reached, demonstrating the effect of the rotation of the rolling ball.
    FS2

  • D1-55: ROTATING ELASTIC RINGS

    D1-55
    Demonstrate "centrifugal reaction" and to indicate why the earth is oblate.

    We have a pair of thin steel rings mounted on a rotating base. The top of the rings is free to slide along its axis, while the bottom is fixed to the rotating base.

    Turning the crank causes the elastic rings to rotate about the vertical axis. The rotation mechanism here uses the mechanical advantage of a large cranked wheel driving a smaller pulley to give the rotating rings a very high angular velocity.

    Engagement Suggestion
    Before rotating at high speed, invite students to predict what will happen to the rings when you get it spinning as fast as you can. Will they:
    • a) keep their circular shape
    • b) flatten at the top and bottom and bulge in the middle
    • or c) extend upwards and grow narrower in the middle?
    Afterwards, encourage students to relate this to other physical phenomena.
    Background
    As the rings rotate, their form distorts, growing wider around the center and flattening at the top and bottom. Interestingly, this is not due to a true outward force acting on the metal at this point, but is an artifact of its rotating reference frame and the forces acting to keep it moving in a circle. This is often termed a centrifugal reaction or centrifugal force, though it is technically a pseudo-force arising from the reference frame.

    This effect is seen in astronomy and geography, as rotating planets, stars, and other bodies take on similarly oblate spheroidal forms.
    D1

  • D1-61: Rolling versus Sliding

    D1-61
    Applies conservation of energy to a rolling object

    An aluminum cylinder rolls down an inclined plane. An identical aluminum cylinder has tiny bearings on one end, so that it slides without friction down the incline.

    Invite the students to make a prediction: If the two cylinders are started from the top at the same time, will the rolling cylinder or the sliding cylinder reach the bottom of the incline first?

    Background
    The two cylinders start at the same height with the same potential energy. As they slide or roll down the ramp, that potential energy is converted into kinetic energy. Linear kinetic energy is proportional to the mass of the cylinder and the square of its velocity. However, the rolling one also has rotational kinetic energy, which is proportional to the moment of inertia of the cylinder and the square of its angular velocity. So for the rolling cylinder, some of the potential energy is converted into rotational kinetic energy as it rolls, and only some of the potential energy is converted into linear potential energy, giving it a lower velocity as it goes down the ramp. So the sliding cylinder reaches the bottom first.
    D1, FS2

  • D1-62: CONSERVATION OF ENERGY IN ROLLING BODY

    D1-62
    Demonstrate conversion of gravitational potential energy into translational and rotational kinetic energy.
    The spool slowly rolls down the incline on its smaller radius, converting gravitational potential energy into rotational kinetic energy with a lesser amount of translational kinetic energy. When the spool reaches the bottom, the larger radius rims make contact with the table top, resulting in a sudden transfer of some of the rotational kinetic energy into translational kinetic energy.

  • D1-63: MAXWELL PENDULUM - LARGE

    D1-63
    Demonstrate transformations between gravitational potential energy and rotational kinetic energy.
    Used as a large-scale yo-yo, transformation of energy can easily be observed by a large class. Wind the string around the small spool radius, hold with the axis horizontal, and release. The initial gravitational potential energy is converted primarily into rotational kinetic energy, with a lesser amount of translational kinetic energy, as the device moves downward, with conversion back to gravitational potential energy after the spool reaches its minimum position and moves back upward.

  • D1-64: MAXWELL PENDULUM - SMALL

    D1-64
    Demonstrate transformations between gravitational potential energy and rotational kinetic energy.
    Wind the string up on the small axel, giving the device some initial gravitational potential energy. When released, this gravitational potential energy is converted into rotational kinetic energy, with a lesser amount of translational kinetic energy, as the device moves downward, then converted back as it rises. Two different sizes of small axels are available.

  • D1-65: YO-YO

    D1-65
    Illustrate transformation between various forms of energy and to perform yo-yo tricks.
    Simply holding the end of the string to allow the yo-yo to unwind and wind back up again illustrates transformation between gravitational potential energy and rotational kinetic energy, with a lesser amount of translational kinetic energy. See Demonstration Reference File for further information on yo-yo tricks.

  • D1-81: TRICYCLE

    D1-81
    Illustrate a tricky problem in rotational dynamics.
    A tricycle is "fixed" so that the steering wheel is locked in the forward/backward direction. When a rope is attached to the upper pedal (pictured at left), held parallel to the floor, and pulled, the tricycle clearly moves in the direction of the pull (the forward direction). (See this on an mpeg video by clicking on the picture at the left above.) Q: How will the tricycle move if the rope is attached to the lower pedal, as shown in the second photograph, and gently pulled? A: The tricycle will move forward, in the direction of the pull. This counterintuitive result can be argued qualitatively by viewing the system in the coordinate system of the wheel. Compare the pull with starting the tricycle by sitting on the seat and pulling the lower pedal backward.

  • D1-82: ROLLING FRICTION

    D1-82
    Show the direction of the frictional force when a rolling object is accelerated.
    One of the three cylindrically symmetric rollers is positioned on the base as shown in the photograph. The base has a rubber top surface and rolls almost without friction on small bearings on the horizontal surface below. The cloth web is held horizontally and yanked, causing the roller to move in the direction of the applied force. The frictional reaction force on the cart is indicated by the direction the cart will move when the roller is yanked off. For a solid disc (moment of inertia less than mr^2) the reaction force is in the direction opposite to the pull, and the base will move backward. For a spool rolling on its smaller radius r (moment of inertia greater than mr^2) the reaction force is in the direction of the applied force. For a thin ring (moment of inertia equal to mr^2) there is no reaction force on the base and it will remain motionless. Because the cylindrical shell has a finite thickness there is some reaction force and a slight amount of motion occurs. However, compared with the solid cylinder and the spool the reaction force is minimal.

  • D1-83: SPOOL

    D1-83
    Illustrate a counterintuitive problem in rotational dynamics.
    The cord is wrapped around the smaller radius of a spool and placed on a horizontal surface such that the cord emerges over the top side of the spool, as shown at the left above. When the cord is pulled the spool will move toward the direction of the applied force, the forward direction. Q: When the cord emerges from the bottom side of the spool, as shown at the right, how will the spool move? A: Forward, just as in the previous example. This problem can be varied as follows. Imagine a line along the cord such that when the cord is held up at some large angle this line intersects the floor along the line of contact of the large radius rims of the spool with the floor. If the cord is held below this line, the spool will move toward the applied force, in the forward direction. If the cord is held above this line, the spool will move away from the applied force, in the backward direction. If the cord is pulled along this line, the spool will remain in place and spin. By holding the cord at this angle while you walk, the spool will slide along the floor as you move, so you can "walk the spool."

  • D1-84: SPINNING CYLINDRICAL SHELL

    D1-84
    A counterintuitive demonstration of rotational dynamics.
    A six-inch diameter thin-walled aluminum tube with O-rings tightly wound around each end lies on a long plastic sheet. The plastic sheet is then quickly pulled horizontally out from under the tube. Q: What will the tube do after the plastic sheet has been removed? (a) move to the left, (b) move to the right, or (c) stop and remain where it was when it left the plastic sheet. A: The aluminum tube moves to the left and spins clockwise as the plastic sheet is removed, then very quickly ceases both its spinning motion and its translation after the plastic sheet is gone! One explanation for this uses a conservation of angular momentum argument. As it is yanked out from under the aluminum tube, the plastic sheet applies no net torque to the tube around the point of contact with the plastic sheet, because the distance between the sheet and the tube is zero. Two components of angular momentum around the contact point can be identified: that due to the clockwise rotation of the tube, and that due to the linear velocity of the tube to the left. The net angular momentum of the tube around the point of contact of the tube with the plastic sheet, however, is zero just before the tube leaves the plastic sheet. Likewise, because the plastic sheet is very thin, there is no net angular momentum around the point of contact of the tube with the table just after the tube leaves the plastic sheet. Sliding friction of the o-rings on the tube with the table causes both the rotation and the translation to quickly cease.
    D1

  • D2-01 RING AND DISC ON INCLINED PLANE

    D2-01
    Demonstrates effect of rotational inertia on acceleration of an object

    A solid disc and a thin ring having the same mass and the same radius roll down an incline starting at rest from the same position. The roller with the greater moment of inertia, in this case the ring, rolls more slowly.
    Engagement Suggestion
    • When presenting the demonstration, encourage students to make a prediction before showing the roll. Will the two objects reach the bottom at the same time, or will one get there first? Which one?
    Background
    The effect of rotational inertia on the speed of a rolling object can be confusing to new students, especially those who have just recently internalized the principles of linear motion. Having just un-learned misconceptions about objects in free fall and discovered that objects experiencing the same force fall at the same rate regardless of mass, it can be counterintuitive to realize that the corollary does not apply in rotational motion. The distribution of mass does itself affect the torque on an object and how fast it rolls.

  • D2-02: Miscellaneous Rolling Bodies On Inclined Plane

    D2-02
    Demonstrates effect of rotational inertia on acceleration of an object
    Different objects are rolled from rest down an incline, and their accelerations compared. The acceleration is less for those bodies with the smaller radius of gyration (square root of the moment of inertia per unit mass). Available rollers include rings, discs, and solid spheres of different masses and radii.
    D2, FS1