Lab 5 Circular Motion & Gravity PHY250L
Student Name:
Access Code (located on the underside of the lid of your lab kit):
Lab Report Format Expectations
Utilize college level grammar and formatting when answering text based questions.
Report all equations in a proper mathematical format, with the correct signs and symbols.
Submissions with incomplete or improperly formatted responses may be rejected.
Pre-Lab Questions
1. State the inverse square law in your own words.
The inverse square law basically means that as you move farther from something, like a light or
a planet, the strength of its effect (like gravity or brightness) drops off really fast. If you double
the distance, the effect becomes four times weaker, because it’s divided by the distance
squared.
2. State the equation used to find the average velocity of an object traveling in uniform circular
motion.
𝑣 = 2𝑣𝑣 / 𝑣
where 𝑣 is the velocity, 𝑣 is the radius, and 𝑣 is the period (the time for one full circle)
3. Consider an object in orbit around the earth, such as a man made spacecraft or the moon. Are
these objects accelerating?
Yes, they are accelerating. Even though their speed might stay the same, they are always
changing direction as they go around in a circle, and any change in direction means there’s
acceleration.
,Lab 5 Circular Motion & Gravity PHY250L
EXPERIMENT 1: BALANCING CENTRIPETAL FORCE
Introduction Questions
1. Suppose an object rotates 15 times every 2 seconds. State the equation for the period of an
object in circular motion in variable form, then calculate the period of rotation, ensuring you
include the correct units. You must show your work for credit.
The period (𝑣) is the time it takes to complete one full rotation. In general, you find the period by
dividing the total time (t) by the number of rotations (N):
𝑣=t/N
Here,
t = 2 seconds
N = 15 rotations
𝑣 = 2 s / 15 = 0.133 s (rounded to three decimal places) That
means each rotation takes about 0.133 seconds.
2. In this lab, you will be rotating a mass on one side of a string that is balanced by a second mass
on the other end of the string (Figure 5). If you apply Newton's Second Law of Motion to mass 1,
m1, and mass 2, m2, you can solve for the period of mass 1, which is
√
P=
πg2 r
Below, derive this equation by using Newton’s Second Law. You must show all pertinent algebra
and mathematical steps for credit. Hint: assume m1= 4m2. How is the centripetal force on m1
related to the force of gravity on m2?
The centripetal force needed to keep mass m₁ moving in a circle comes from the tension in the
string. That tension is equal to the weight of the hanging mass m₂.
So,
m₁ * v² / r = m₂ * g
Since v = 2πr / P (where P is the period), substitute:
m₁ * (2πr / P)² / r = m₂ * g
m₁ * 4π²r / P² = m₂ * g
Now, solve for P²:
, Lab 5 Circular Motion & Gravity PHY250L
4π²m₁r = m₂gP²
P² = (4π²m₁r) / (m₂g)
P = 2π * √(m₁r / m₂g)
If m₁ = 4m₂, plug in:
P = 2π * √(4m₂r / m₂g)
P = 2π * √(4r / g)
P = 4π * √(r / g)
Figure 5: Rotating mass.
Data and Observations
Input the time it took to conduct 15 revolutions and the corresponding period into the table below.
Then use the equation in Question 2 of the experiment introduction to calculate the expected value of
the period of rotation. In the final column, calculate a percent error between these two values.
Table 1. Rotational Data
Time per 15 Expected Percent
Radius (m) Period (s)
revolutions (s) Value Error (%)
0.25 12.20s 0.81s 1.00 19%
0.40 13.30s 0.89s 1.27 30%
0.15 8.00s 0.53s 0.78 32%
Insert a photo of the apparatus you built for this experiment. The photo must clearly depict the correct
number of washers and a length of line that is reasonable for the radius you denoted in the above table.
Your photo must also include your handwritten name. Submissions that do not contain a photo with
these requirements will be rejected.
Student Name:
Access Code (located on the underside of the lid of your lab kit):
Lab Report Format Expectations
Utilize college level grammar and formatting when answering text based questions.
Report all equations in a proper mathematical format, with the correct signs and symbols.
Submissions with incomplete or improperly formatted responses may be rejected.
Pre-Lab Questions
1. State the inverse square law in your own words.
The inverse square law basically means that as you move farther from something, like a light or
a planet, the strength of its effect (like gravity or brightness) drops off really fast. If you double
the distance, the effect becomes four times weaker, because it’s divided by the distance
squared.
2. State the equation used to find the average velocity of an object traveling in uniform circular
motion.
𝑣 = 2𝑣𝑣 / 𝑣
where 𝑣 is the velocity, 𝑣 is the radius, and 𝑣 is the period (the time for one full circle)
3. Consider an object in orbit around the earth, such as a man made spacecraft or the moon. Are
these objects accelerating?
Yes, they are accelerating. Even though their speed might stay the same, they are always
changing direction as they go around in a circle, and any change in direction means there’s
acceleration.
,Lab 5 Circular Motion & Gravity PHY250L
EXPERIMENT 1: BALANCING CENTRIPETAL FORCE
Introduction Questions
1. Suppose an object rotates 15 times every 2 seconds. State the equation for the period of an
object in circular motion in variable form, then calculate the period of rotation, ensuring you
include the correct units. You must show your work for credit.
The period (𝑣) is the time it takes to complete one full rotation. In general, you find the period by
dividing the total time (t) by the number of rotations (N):
𝑣=t/N
Here,
t = 2 seconds
N = 15 rotations
𝑣 = 2 s / 15 = 0.133 s (rounded to three decimal places) That
means each rotation takes about 0.133 seconds.
2. In this lab, you will be rotating a mass on one side of a string that is balanced by a second mass
on the other end of the string (Figure 5). If you apply Newton's Second Law of Motion to mass 1,
m1, and mass 2, m2, you can solve for the period of mass 1, which is
√
P=
πg2 r
Below, derive this equation by using Newton’s Second Law. You must show all pertinent algebra
and mathematical steps for credit. Hint: assume m1= 4m2. How is the centripetal force on m1
related to the force of gravity on m2?
The centripetal force needed to keep mass m₁ moving in a circle comes from the tension in the
string. That tension is equal to the weight of the hanging mass m₂.
So,
m₁ * v² / r = m₂ * g
Since v = 2πr / P (where P is the period), substitute:
m₁ * (2πr / P)² / r = m₂ * g
m₁ * 4π²r / P² = m₂ * g
Now, solve for P²:
, Lab 5 Circular Motion & Gravity PHY250L
4π²m₁r = m₂gP²
P² = (4π²m₁r) / (m₂g)
P = 2π * √(m₁r / m₂g)
If m₁ = 4m₂, plug in:
P = 2π * √(4m₂r / m₂g)
P = 2π * √(4r / g)
P = 4π * √(r / g)
Figure 5: Rotating mass.
Data and Observations
Input the time it took to conduct 15 revolutions and the corresponding period into the table below.
Then use the equation in Question 2 of the experiment introduction to calculate the expected value of
the period of rotation. In the final column, calculate a percent error between these two values.
Table 1. Rotational Data
Time per 15 Expected Percent
Radius (m) Period (s)
revolutions (s) Value Error (%)
0.25 12.20s 0.81s 1.00 19%
0.40 13.30s 0.89s 1.27 30%
0.15 8.00s 0.53s 0.78 32%
Insert a photo of the apparatus you built for this experiment. The photo must clearly depict the correct
number of washers and a length of line that is reasonable for the radius you denoted in the above table.
Your photo must also include your handwritten name. Submissions that do not contain a photo with
these requirements will be rejected.
