Worksheet #6
Chapter 6 – Circular Motion, Orbits, & Gravity
Terms, Definitions, Vocab
Uniform Circular Motion Frequency
Period
Centripetal Force
Law of Gravity
Orbits
v2
ac 
r
f 
1
T
g planet
2 r
Gm1m2
 2 fr
G  6.67 1011 Nkgm
F1,2  F2,1 
T
r2
GM planet
GM
 4 2  3
2
v


T


r
2
r
R planet
 GM 
v
2
2
Skills & Concepts
1. Chapter 6 starts by re-defining centripetal acceleration, which is first introduced in section
3.8, and then uses that acceleration term with Newton’s 2nd Law, which is discussed all over
chapters 4&5, but most focused in section 5.2. It is worth reviewing these sections as part of
your preparation for this chapter.
2. If a turn-table is spinning at a frequency of 45 rpm (revolutions per minute), what is its period
of rotation in seconds?
3. What direction does the net force point for an object experiencing uniform circular motion?
4. What direction is the force by the Earth on the Moon? Should this scare you?
5. There are two constants defined by the letter G, one capital and one lower-case. Which of
them is the same on Mars and on Earth?
6. When studying the orbit equations presented in section 6, pay particular attention to which
mass the variable ‘M’ [Capital M] represents.
7. If the Moon were replaced with a baseball, how would its orbital period and velocity change?
8. If the Earth were replaced with a baseball, how would the Moon’s orbital period and velocity
change?
Example Problems
Fill in the blank boxes for each problem. The boxes on the left contain mathematical steps,
while the boxes on the right contain brief explanations of the step
Example 6.2
List Known and Desired Quantities
Convert given quantities into desired Units
Solve for Period
v  2 fr  2 (60 Hz )(0.125 m)
v  47 ms
Use the above value to solve for acceleration
How does the acceleration you found compare to the gravitational acceleration? If the saw
blade was bigger (larger radius) would the same frequency produce a larger or smaller speed?
And a larger or smaller centripetal acceleration?
Example 6.7
List Known and Desired Quantities
 Fnet  y  ma y
NTrack ,Car  WEarth ,Car  0
NTrack ,Car  mg
Use Newton’s 2nd Law I the horizontal
direction, and the definition of centripetal
acceleration, to create an expression that
includes the velocity of the car
Write an expression for the maximum static
friction force on the car
Use the above expression, and the values
given to solve for the maximum speed
Does this maximum speed depend on the mass of the car? If we instead took a wider, 40-m
radius turn, how much larger would the maximum speed be?