1. Forces and circular motion
Centripetal (turning) acceleration
Tangential (speed up/down) acceleration
Total acceleration: always in the direction of the total force
Demo: pendulum animation

3. The object is slowing down

4. Circular and rolling motion
vcenter =Rw
If angles are all in radians:
s along arc at any r s(r) = r q
v tangential at any r v(r) = rw
a tangential at any r aT(r) =r a
If rolls without slipping and angles are all in radians:
s linear (or translational) Dx = Rwheel q
v linear (or translational) vcenter = Rwheel w
a linear (or translational) acenter = Rwheel a
acenter =Ra

5. Circular (angular) kinematic equations
Draw pictures and choose a direction for + angles, rotations.
Can use units of rev/sec, deg/sec or rad/s if you use them for each term in these eqns.
You must use radians if you want to use the relation s=rθ, v=rw and a=ra.

6. Circular (angular) kinematic equations
Friction slows down a spinning top with angular deceleration of 2 rad/s2. It was initially spinning at 50 rad/s.
How many revolutions will it turn before stopping?

7. Newton’s 2nd law for circular motion
General hints for forces on objects moving in a circle:
Choose + radial direction toward center (along ac­)
Draw FBD of object showing only real forces (don’t treat ac as a force)
Write
At what maximum speed can you take a turn of radius r if the friction coefficient is m?
Lagoon Funhouse ride

8. Banked roadways How does a banked road help us turn?
It’s best here to keep x along horizontal, y vertical because…
Find N and f

9. Ferris Wheel and forces
Draw forces on a rider at top, bottom and sides. Which of these changes strength during the turn? Assume constant v.

10. Motion on outside top of a vertical circle
Find the normal force on a car moving at v at the top of a hill, radius r.
What happens if you go too fast?

11. Motion on inside top of a vertical circle
Find the normal force on a car moving at v at the top of a hill, radius r.
What’s different here?
What happens if you go slow fast?

12. Motion on inside bottom of a vertical circle
P4. Which equation is correct? a) b) c)

13. Conical pendulum: horizontal circle
P4. Which two equations are correct?
a) 1 and 3
b) 1 and 4
c) 2 and 3
d) 2 and 4

14. P5. You are moving a ball on a string in a circle around your head
P5. You are moving a ball on a string in a circle around your head. If you keep the same speed v for all lengths of the string, the string will most likely break
A. when the string is short
B. when the string is long
C. neither (same for both short and long)