UNIVERSITY PHYSICS I CHAPTER 10 Chapter 10 Spin and orbital motion Rotation: All around us: wheels, skaters, ballet, gymnasts helicopter, rotors, mobile engines, CD disks, Atomic world: electrons“spin”,“ orbit Universe: planets spin and orbiting the sun galaxies spin,… Chapter 4 kinematics Chapter 10 dynam
1 Chapter 10 Spin and orbital motion Rotation: All around us: wheels, skaters, ballet, gymnasts, helicopter, rotors, mobile engines, CD disks, … Atomic world: electrons— “spin”, “orbit”. Universe: planets spin and orbiting the sun, galaxies spin, … Chapter 4 kinematics Chapter 10 dynamics
s10.1 Some concepts about rotation 1. Spin--describe rotational motion of a system about an axis through its center of mass 2. Rigid body-a system composed of many pointlike particles that maintain fixed distances from each other at all time each particle of the spinning rigid body system executes circular motion about the axis through the center of mass 3. Orbital motion-the center of the mass of system is moving in space from a perspective t a particular reference frame. 810.1 Some concepts about rotation The motion of the center of mass must not be circular ●
2 §10.1 Some concepts about rotation 1. Spin—describe rotational motion of a system about an axis through its center of mass. 2. Rigid body—a system composed of many pointlike particles that maintain fixed distances from each other at all time. each particle of the spinning rigid body system executes circular motion about the axis through the center of mass. 3. Orbital motion—the center of the mass of the system is moving in space from a perspective of a particular reference frame. The motion of the center of mass must not be circular. §10.1 Some concepts about rotation
s10.1 Some concepts about rotation 4. The orbital angular momentum of a particle Define:L=r×p=rxm Magnitude L L=rmvsin8=Pr=rp Direction: Perpendicular to the plane containing the 6∴ r and p 810.1 Some concepts about rotation Notice O L is measured with respect to the origin at O; ②unit:kgm2/s; 3 whatever the path or trajectory of a particle is straightline. curved path, closed orbital ath 5. The angular momentum of the circular orbital motion of a particle (a) Angular momentum
3 4. The orbital angular momentum of a particle Define: L r p r mv r r r r r = × = × x y z m θ r r p r o ⊥r L r ⊥ p Magnitude: L = rmvsinθ = p⊥r = r⊥ p Direction: r p r r and Perpendicular to the plane containing the §10.1 Some concepts about rotation Notice: 1 is measured with respect to the origin at O; 2 unit: kg·m2/s; 3 whatever the path or trajectory of a particle is straightline , curved path, closed orbital path, …. L r 5. The angular momentum of the circular orbital motion of a particle (a) Angular momentum §10.1 Some concepts about rotation
s10.1 Some concepts about rotation L=rxp=r×m L= myr V=xI v=⑦r then mor=mro L=mro (b)Moment of inertia of a particle define = mr then L=mro=lo 810.2 The time rate of change of angular momentum and torque 1. The time rate of change of angular momentum for a single particle L=r×P P) X D+rx dt dt dt d p=×p=vxmv=0 F dt dL =rX d rxF dt total
4 L mvr L r p r mv = = × = × r r r r r v r v r ω ω = = × r r r r r p r o m ω r ω ω 2 2 then L = m r = mr (b) Moment of inertia of a particle ω r r 2 L = mr §10.1 Some concepts about rotation 2 I = mr ω ω r r r L = mr = I 2 define then §10.2 The time rate of change of angular momentum and torque 1. The time rate of change of angular momentum for a single particle t p p r t r r p t t L d d d d ( ) d d d d r r r r r r r = × = × + × L r p r r r = × total d d d d 0 d d r F t p r t L p v p v mv t r r r r r r r r r r r r Q ∴ = × = × × = × = × = r r F r θ o m
810.2 The time rate of change of angular momentum and torque 2. torque Define: T total=/ F total Magnitude t=rF sin 0=n F=rF1=d' Direction: Perpendicular to the plane containing the r and F Unit of the torque: n'm r is the position vector of the point of application of the force with respect to the chosen origin 8 10.2 The time rate of change of angular momentum and torque Discussion: F 6=0or丌, If 3 F=0 total total =0 F cross the O
5 Define: total Ftotal r r r r τ = × 2. torque is the position vector of the point of application of the force with respect to the chosen origin. r r Unit of the torque: N·m Magnitude: = = ⊥ = ⊥ τ rF sinθ r F rF Direction: Perpendicular to the plane containing the r F r r and r r F r θ o m r⊥ = d F⊥ §10.2 The time rate of change of angular momentum and torque r r F r θ o m r⊥ = d F⊥ If cross the , 0, 0 or , total F O Fr r = θ = π 0 τ total = r §10.2 The time rate of change of angular momentum and torque Discussion: