Linear & Angular Relationship Lab
Purpose:
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Name:__________________________________
Date:____________
Mod:____________
To determine the relationship between linear and angular quantities of a rolling object.
Materials:
- Masking Tape Roll (other circular object)
- Incline Plane
- Stopwatch
Theory:
The linear velocity of a rotating object is equal to the radius of the rotating object multiplied by
its angular velocity. The linear acceleration of a rotating object is equal to the radius of the rotating
object multiplied by its angular acceleration. The distance traveled by a point on the outside edge of a
rotating object is equal to the radius of the rotating object at the specific point and the angular
displacement measured in radians. Angular displacement can be described as the measure of change in
a rotating object where the units are in radians. The equations of linear velocity, linear acceleration and
the arc length are shown below:
𝑣 = 𝑟𝜔
𝑎 = 𝑟𝛼
𝑠 = 𝑟𝜃
Procedure:
1. At the lab station, set up a shallow incline using a few textbooks to prop up the incline plane.
2. Measure the angle of the incline using the meter stick and some trigonometry. Record the angle
in the table below.
3. Using a pencil, place a mark on the outside edge of the roll of tape and a mark at the top of the
incline. Place the roll of masking tape on the incline with the two marks in contact with one
another.
4. Slowly roll the tape down the incline with your hand as a guide. Make three complete rotations
and measure the distance traveled after the third rotation in meters. Place a mark on the
incline with the pencil at this location. Record the distance in the table below.
5. Measure the radius of the tape roll in meters and record the radius in the table below.
6. Place the tape at the same spot as step #3 and time the roll of tape as it travels the same
distance you measured in step#4.
7. Repeat step #6 for a total of five trails. Once the five trails are completed, calculate the average
time to roll down the incline to the mark on the incline where three rotations took place.
Record the values of time in the table below.
8. Using the angle of the incline, calculate the theoretical acceleration of the roll of tape down the
incline. Use the following equation and record the value in the table below: 𝑎 = 𝑔 sin 𝜃
9. Using the average time, calculate the linear acceleration of the tape using the equation below:
𝑑 = 𝑣𝑖 𝑡 + 12𝑎𝑡 2 , where 𝑣𝑖 = 0𝑚𝑠. The distance should be the distance rolled down the incline
after three rotations, which was found in step #4. Record the experimental linear acceleration
in the table below.
10. Using the answer found in step #9, calculate the angular acceleration using the following
equation and record: 𝑎 = 𝑟𝛼
11. Using the angular acceleration that was just found and the average time, calculate the angular
displacement using the following equation and record: 𝜃 = 𝜔𝑖 𝑡 + 12𝛼𝑡 2
Linear & Angular Relationship Lab
Methacton High School Physics Department
1
Data:
Angle of
Incline (°)
Distance for
3 Rot (m)
Radius (m)
Trail #1
Trial #2
Trail #3
Trial #4
Trial #5
Average
Time (s)
Theoretical
Linear
Acceleration
(m/s2)
Experimental
Linear
Acceleration
(m/s2)
Experimental
Angular
Displacement
(θ)
Theoretical
Angular
Displacement
(θ)
Angular
Acceleration
(rad/s2)
6π rad
Post-Lab Questions:
1. How does the experimental angular displacement found in step #11 compare to theoretical
angular displacement of 6𝜋 rads, which is the angular displacement for 3 complete rotations?
2. What is the percent error between the actual angular displacement and the experimental
angular displacement?
3. What factors influence any errors between the experimental and the actual angular
displacement?
4. How does the theoretical and experimental linear accelerations compare?
5. Does the moment of inertia affect the rotation of the tape down the incline? Explain.
6. If a solid cylinder was used instead of a roll of tape, would that affect the data collected in the
experiment? Explain.
Linear & Angular Relationship Lab
Methacton High School Physics Department
2