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Rotational Dynamics

  • B2-21: CONCEPT OF TORQUE - TORSIONAL CHAIR

    B2-21
    Introduce the concept of torque

    A rigid scale is attached to the torsional chair (with its internal coil spring attached to provide a countering force). An arbitrary force (measured by the spring scale) can be exerted at an arbitrary angle (measured by the protractor) at an arbitrary distance from the center of the chair (measured by the scale) to produce some arbitrary rotation of the chair against its restoring spring. Equal torques can be applied in several different ways, or torques can be scaled by changing one or more of the variables. Measurements are good to about ten percent.

    The photographs above show the chair being rotated about 180 degrees by an external torque, which is created by a force perpendicular to the radius vector (center) or at an angle of 45 gegrees with respect to the radius vector (right).

    Note that this demonstration and demonstrations B2-22 and B2-32 use many of the same components.
    FS0, OS0, B2

      

  • B2-31: EQUILIBRIUM OF TORQUES - WHEELS AND AXLES

    B2-31
    Demonstrate equilibrium of torques

    Two wheel and axle assemblies are provided. For each, there are cylinders of smaller radius r and larger radius R. A smaller weight m is suspended from a string wrapped around the larger radius R, and a larger weight M suspended from the smaller radius r. For equilibrium of torques:

    mR = Mr.

    On this model, radius ratios of 2:1 and 4:1 are available. A set of additional masses can be provided to vary the load.
    FS2

  • C4-13: ACCELEROMETER ON ROTATOR

    C4-13
    Show that the surface of a rotating liquid assumes a parabolic shape.
    This is the accelerometer from C4-12 mounted on a hand-cranked rotator. Rotate the accelerometer at a constant rate to show the parabolic surface. (A video camera can be provided in the lecture halls if needed.)
    C4, D1

  • C6-12: SKIDDING AUTOMOBILE

    C6-12
    Demonstrate the effect of locked wheels on vehicle stability.

    A plastic toy car is lightweight enough that its wheels can, when needed, be locked with a simple piece of masking tape. When the wheels are locked, it skids rather than rolling freely; but its behaviour when skidding depends on which wheels are locked.
    Engagement Suggestion
    • Challenge students to make a prediction about how the car will behave with front or back wheels locked before performing each phase of the experiment.
    • With both sets of wheels free, push the car across the floor; it moves in a straight line with the orientation in which it was pushed.
    • With the front wheels locked and the rear wheels free, it will also continue in the normal forward orientation, slowly skidding to a halt.
    • With the rear wheels locked and the front wheels free, however, when pushed in the forward direction it will rotate so that it moves backward .
    • Students may ask what happens if all four wheels are locked. Encourage them to make predictions based on what they've seen here, and on what other systems the resulting wheelless mass would resemble.
    Background
    Because rolling (static) friction is generally greater than sliding friction, whichever set of wheels is sliding will end up in the forward direction. In real vehicles, this can be the cause of serious accidents!
    C6

  • C7-42: AIR TABLE - COLLISIONS OF PUCKS

    C7-42
    Qualitatively demonstrate elastic and inelastic two-dimensional collisions.
    Two or more pucks can be used to demonstrate elastic collisions. Velcro collars on pucks (front row of second picture) produce perfectly inelastic collisions. The air table is only available in rooms 1410, 1412, and 0405 because it will not fit through a standard single door. In smaller rooms, please consider C7-43 or C7-44.

    Also see a simulation of similar collisions here: https://www.myphysicslab.com/engine2D/billiards-en.html

  • C7-44: COLLISIONS - HOVERPUCKS

    C7-44
    Demonstrate two-dimensional collisions.
    Two battery-powered hoverpucks, as shown. Can be used to demonstrate a variety of two-dimensional collisions and motion. Velcro collars are available for inelastic collisions.

    Also see a simulation of similar collisions here: https://www.myphysicslab.com/engine2D/billiards-en.html

    C7

  • D1-01 STROBOSCOPE AND FAN

    D1-01
    Demonstrates rotational motion using stroboscope
    The motion of a fan can appear to slow down, stop, or "reverse" with the use of the stroboscope, an instrument that emits intense bright light at different frequencies. Questions: What will it look like when the frequency of the stroboscope is faster than the rotating speed of the fan? When it has the same speed as the fan?
    OS6, LS1

  • D1-02: PELLET VELOCITY FROM ROTATING DISCS

    D1-02
    Determine the speed of a B-B using rotational kinematics.
    A B-B is shot from the air gun with a linear velocity v, such that it passes between the two rotating discs which have a separation d and are rotating with an angular velocity w. The angle a that the two discs rotate while the B-B is traveling between them is determined by inspecting the two discs. The velocity of the B-B is then determined by using the relation: v = w d / a. In this case the angular velocity w of the rotating discs is 1800 rpm, and the distance d between the discs is 1 meter. CAUTION: Lift apparatus by handles only. Pump just before firing to assure uniform velocity for several trials. See also Demonstrations C7-51: BALLISTIC PENDULUM - PELLET GUN and C7-53: AIR TRACK - SPEED OF AIR GUN PELLET for other ways to determine the B-B velocity.

  • D1-11: CYCLOID - LIGHT BULB ON WHEEL

    D1-11
    Demonstrate cycloidal motion.
    Turn off room lights, turn on light bulb at perimeter of roller, and roll device to create lighted cycloidal path.
    D2

  • D1-12: ADDITION OF ANGULAR VELOCITIES

    D1-12
    Illustrate the complex motion resulting from addition of two angular velocities.
    The rotating disc with the lamp attached to its perimeter can spin in its mount on low-friction bearings. Simultaneously, the mount can be rotated by hand. As the light bulb rotates about the two axes it traces out a complicated motion which is the sum of two angular velocities.
    D1

  • D1-21: ANGULAR VELOCITY - OBERBECK CROSS

    D1-21
    Measure the angular velocity of a rotating object.
    Various masses M can be hung on a string wound around an axle of either of two radii R to provide a torque T = MgR. Four brass masses m can be positioned along the arms at one of four distances l from the axis of rotation to provide a moment of inertia I = 4ml^2. The angular acceleration a = T/I = MgR/4ml^2 can then be calculated. The angular acceleration can be determined experimentally by measuring the time required for the system to rotate one complete revolution starting from rest: a = 2 d/t^2, where t is the time required for the device to rotate through the angle d in radians. The angular velocity can be determined by simply measuring the time per revolution.
    FS1, ME1

  • D1-30: TRAJECTORY FROM CIRCULAR ORBIT - OVERHEAD PROJECTOR

    D1-30
    Show that the instantaneous velocity of an object executing uniform circular motion is tangent to the circle.
    A marble is rolled around the inside of the circular band on an overhead projector. When the ball leaves the end of the circular segment it will travel in the direction tangent to the circle at the point where it leaves.

    A transparent sheet is available with an outline of the circle and various possible paths. This can be used to challenge the students to guess the outcome of the experiment before performing it.

    Compare D1-31 and D1-32, other demonstrations showing similar effects.
    D1

  • D1-31: TRAJECTORY FROM SPIRAL

    D1-31
    Show that forces are required to create circular motion.
    The apparatus pictured is positioned on a horizontal surface. A small ball bearing (in container at lower left of picture) is blown through the spiral hose, emerging at the right side and moving downward (in the picture), toward one of the five aluminum tube targets. Ask your students to predict: Which of the targets will it hit, and why?

    Consider using in conjunction with D1-30 or D1-32 to show the effect in a less complex scenario.
    OS10

  • D1-32: TRAJECTORY FROM CIRCULAR ORBIT

    D1-32
    Show that the instantaneous velocity of an object executing uniform circular motion is tangent to the circle.
    A pool ball is rolled clockwise around the inside of the circular band. When the ball leaves the end of the circular segment it will travel in the direction tangent to the circle at the point where it leaves. Consider placing tape markers on the table or floor and having students predict which direction it will go before performing the experiment. Have them justify their conclusions, then discuss the results afterwards.

    Compare D1-30 and D1-32, which show similar effects.
    D1

  • D1-33 ROTATING MASS ON STRING

    D1-33
    Illustrates centripetal force and that instantaenous velocity is tangent to the circular path
    Swinging the ball around one's head demonstrates uniform circular motion. If the string is released, its initial trajectory is tangent to the circular path
    D1

  • D1-34 ROTATING MASS ON SPRING

    D1-34
    Illustrates centripetal force
    Swinging the ball around one's head will cause the spring to extend, indicating the spring is under tension -- the centripetal force on the ball. By rotating the ball faster, the spring will extend more
    D1

  • D1-35 CENTRIPETAL FORCE - ROTATING MASS

    D1-35
    Measures the required centripetal force for an object to move with uniform circular motion
    A one-kilogram mass is rotated at a constant angular velocity by a motor-driven pulley. The centripetal force is measured by passing the radial string holding the mass around a pulley in the central tube and connecting it up the vertical tube to the spring scale. The angular velocity can be varied by rotating a knob on the front of the motor. The centripetal force can be calculated by measuring the angular velocity with a digital clock or a manual timer (available upon request).
    OS11

  • D1-36: AIR TABLE - CENTRIPETAL FORCE

    D1-36
    Show that centripetal force varies with angular velocity.
    A string connects the rotating mass on the air table past a pulley to the spring scale. The centripetal force can be determined using the measured values of mass, rotational period and radius, then compared with that read from the spring scale. The period can be measured using the manual timer, if desired. Not available in small classrooms because it will not fit through a standard door.

  • D1-37 MUDSLINGER

    D1-37
    Illustrates centripetal force and that instantaenous velocity is tangent to the circular path
    A small glob of putty is stuck to the edge of a rotating disc. As the angular velocity is increased, at some point the force holding the putty will no longer be sufficient to provide the necessary centripetal force, and the putty leaves the rotating disc, moving tangentially away from the point of release.

    This is a purely qualitative demonstration; to make measurements, try D1-35.
    D1

  • D1-39: PENNY AND COAT HANGER

    D1-39
    Demonstrate centripetal force and centrifugal reaction in a dramatic way.
    Balance the penny (face up) on the flattened coat hanger tip, as shown in the photograph. Start slowly swinging the hanger back and forth like a pendulum, then rotate it in a complete circle. With practice, it is possible to rotate the system several times and stop the motion without dislodging the penny.
    D1