Gyroscopes Lecturer: Professor Stephen T. Thornton

Reading Quiz The position vector from the axis to where a force is applied to a wheel is and the force vector is . In what direction is the torque? A) B) C) D) E)

Answer: E

Last Time Angular momentum and torque system of particles rigid objects Unbalanced torque Kepler’s 2nd law

Today Angular momentum and torque Gyroscopes Inertial forces, pseudoforces Review

Struck Think Rod. A thin rod of mass M and length rests on a frictionless table and is struck at a point from its CM by a clay ball of mass m moving at speed v. The ball sticks to the rod. Determine the translational and rotational motion of the rod after the collision. Giancoli, 4th ed, Problem 11-51

The Right-Hand Rule for Torque

Torque and Angular Momentum Vectors

The Torque Exerted on a Gyroscope Do demo.

Precession of a Gyroscope

The Spinning Top and Gyroscope A spinning top will precess around its point of contact with a surface, due to the torque created by gravity when its axis of rotation is not vertical. Do the frictionless demo and use drill to spin top. Make sure I spin it in the way shown here. Also try to spin a spinning top. Note that a right hander will spin it in the opposite direction as shown here.

The Spinning Top and Gyroscope The angular velocity of the precession is given by: This is also the angular velocity of precession of a toy gyroscope, as shown previously.

Uses of Gyroscopes Navigation has largely been superseded by GPS, but still useful for stabilizers Satellites – example is Hubble Space Telescope Virtual Reality helmets – used to discern person’s motion Racing cars – engine is a gyroscope Bicycles and motor bikes Robot orientation See http://www.gyroscopes.org/uses.asp for some descriptions.

Rotating Frames of Reference; Inertial Forces An inertial frame of reference is one in which Newton’s laws hold; a rotating frame of reference is noninertial, and objects viewed from such a frame may move without a force acting on them. Figure 11-25. Path of a ball released on a rotating merry-go-round (a) in the reference frame of the merry-go-round, and (b) in a reference frame fixed on the ground.

Rotating Frames of Reference; Inertial Forces There is an apparent outward force on objects in rotating reference frames; this is a fictitious force, or a pseudo force. The centrifugal “force” is of this type; there is no outward force when viewed from an inertial reference frame.

Show two videos Skateboard aerials Figure skater These two flash videos are on my Home directory. Both are good. The figure skater video is 2:30 long, discusses torque, etc. Skateboard aerial is 3 min.

Rolling Tire. A boy rolls a tire along a straight level street Rolling Tire. A boy rolls a tire along a straight level street. The tire has mass 8.0 kg, radius 0.32 m and moment of inertia about its central axis of symmetry of 0.83 kg m2. The boy pushes the tire forward away from him at a speed of 2.1 m/s and sees that the tire leans 12° to the right. (a) How will the resultant torque affect the subsequent motion of the tire? (b) Compare the change in angular momentum caused by this torque in 0.20 s to the original magnitude of angular momentum. Giancoli, 4th ed, Problem 11-71

Conceptual Quiz A student sits on a spinning stool with her arms folded. When she extends her arms away from her body, her kinetic energy Increases Decreases Stays the same Depends on her mass Need further information

Conceptual Quiz Decreases Angular momentum is conserved. Rotational inertia is increased. How is this possible? What happened to the energy? Is conservation of energy violated? increases

Conceptual Quiz A student sits on a spinning stool with her arms folded. When she extends her arms away from her body, her kinetic energy B) Decreases Why? Some of the kinetic energy is converted to potential energy, because her arms are extended!

Conceptual Quiz The name of the quantity which is greater for a long 70 kg barbell than for a short 75 kg barbell that makes it harder for us to hold and twist it is called rotational kinetic energy momentum inertia mass center of mass

Conceptual Quiz The name of the quantity which is greater for a long 70 kg barbell than for a short 75 kg barbell that makes it harder to twist is called rotational C) inertia

Conceptual Quiz A wheel of outer radius R has an axle of radius R/6 Conceptual Quiz A wheel of outer radius R has an axle of radius R/6. Strings are wrapped as shown around the rim of the wheel and around the axle. If the string around the rim of the wheel has tension T, what must be the tension T’ in the string around the axle in order for the wheel to not move? T’

Answer: A) 6T We want torque = 0

Dropping Disk. A nonrotating cylindrical disk of moment of inertia I is dropped onto an identical disk rotating at angular speed ω. Assuming no external torques, what is the final common angular speed of the two disks? Giancoli, 4th ed, Problem 11-15