F acceleration, a  angular acceleration,  m/sec 2 radians/sec 2 or degrees/sec 2 We’ve seen our “equations of motion” complemented by descriptions of spinning and rotation: Recall: (linear) momentum: mv = constant m/sec (linear) momentum: I  = constant radians/sec

F gravity The moon is always “falling”, but - Never changes speed: No increase in Kinetic Energy! - Never gets any closer to the earth: No decrease in Potential Energy!

Center of mass/ center of balance

F grav N N N N

A tricycle provides a large base and ordinarily a rider’s center of mass is comfortably within its boundaries. f vv f v But a child’s inertia can carry them too easily outside that bounds on a fast turn.

Note the low center-of-mass for riders of a Big Wheel

What helps keep a bicycle steady?



This unicyle is being ridden past you to the left. By the right-hand-rule, the angular momentum of the wheel points A. right.B. left. C. down.D. up. E. into the screen. F. out of the screen.

rotational mass somewhat large since some body parts are held out at large distances r i from the center. now all body parts are held in at small r i from the center. I 1  1 = I 2  2

This motorcyclist is A. falling down. B. making a left turn. C. making a right turn.

W N f N f total force from road surface on motorcycle

N f But what about the torque gravity applies? The total surface forces are not off-centered at all so produce no net torque of their own!

 If this wheel started to tip to the left: This would be due to a torque (applied by gravity) By the right-hand-rule, this torque points in what direction? A. right.B. left. C. down.D. up. E. into the screen. F. out of the screen.

 A torque of course produces a change in angular momentum: This change will be in the direction of the torque (out towards you in this picture).  '' the new angular momentum What does this mean? This gyroscopic precession will actually steer the wheel naturally to the left!

Head-on elastic collisions: V of equal masses: What happens in a head-on collision with a much heavier mass?

V

V ~V

What about the (more common) glancing blow? Remember: contact forces are NORMAL forces! To understand what effect this has, consider bouncing a ball off the ground…

A glancing blow with the ground is like partly traveling straight down into it and, at the same time, trying to travel past it. This part of its motion (the downward component of its velocity) is reversed by the collision, just like a head-on collision event. The horizontal component of its motion is unaffected!

F. With the fingers of your right hand curled in the direction of the rotating wheel, your thumb will point out of the screen. B. He is leaning to turn to his left. F. out of the screen. The direction a torque twists is defined by the same right- hand rule. When screwing in an ordinary (right-hand threaded) screw, with screw- driver in right hand, your fingers curl in the direction you’re twisting, and your thumb points in the direction you’re driving the screw (the direction of the torque). Sure, the initial angular momentum of the spinning wheel is to the left. But the torque that’s trying to tip the wheel is rotating it so that the top of the wheel falls over to the left…a counter-clockwise twist of the top over the bottom edge which is against the ground.