Rotational inertia by rolling down an incline.
VIEW THE VIDEO OF THE EXPERIMENTS BEING PERFORMED AND RECORD THE DATA FROM THE VIDEO. USE THIS DATA TO CALCULATE THE MOMENT OF INERTIA AND WRITE YOUR REPORT.
Video-1:
Measurements of diameters, masses and angle of incline: https://youtu.be/UlyfoLZEDiY
Video-2:
Measurements of time for objects to roll down the incline: https://youtu.be/KwKOfROqqqo
EQUIPMENT:
Inclined Plane
Meter stick
Cylinders, spheres
Stopwatch
Vernier Caliper
Triple beam balance
Using Equations 1 through 4, we can derive the following for the measured value of Rotational Inertia:
Procedure:
Watch the videos in the given link.
From Video-1, record the masses and diameters of the cylinder and solid sphere. The diameters of the rings are taken several times since they are relatively flexible objects. Take their average values.
From Video-1, record the length of the inclined plane and the height at two end points to obtain the slope. The heights are measured several times. Take their average value.
From Video-2, for each rolling object, record the travel time from A to B and fill them into the data table. Note that some rolling motions result in the object colliding with the side, or falling off the incline. Do not use that data.
Data:
Mass and Diameters:
NO OBJECT MASS DIAMETER ROTATIONAL INERTIA FROM EQN. 5
UNITS
1 Cylinder-1: Copper
2 Cylinder-2: Aluminum
3 Cylinder-3: Plastic
4 Cylinder-4: Brass
5 Solid Sphere-1: Plastic
6 Solid Sphere-2: Steel
Inner outer
7 Ring-1: Heavy Tape
8 Ring-2: Light Tape
Obtaining the Angle of Incline θ:
Average Height of plank on higher side: ___________
Average Height of table on lower side: ___________
Length of Table: ______________ Calculated angle θ: __________________
Obtaining the Descending Height, h :
Distance traveled from A to B: _____________ Descending height: _________________
Object Time Rotational Inertia
(equation 6) Rotational Inertia
(equation 5) % error
No Final time Initial time Travel time t Average travel time t
units
Cylinder-1 copper 1
2
3
Cylinder-2
Aluminum 1
2
3
Cylinder-3
Plastic
Cylinder-4
Brass
Solid Sphere-1
Plastic
Solid Sphere-2
Steel
Ring-1
Heavy Tape
Ring-2 Light Tape
Calculations:
Calculate the average travel time for each object.
Input the average travel time into Equation 6, and calculate the object’s moment of inertia.
Use Equation 5 to calculate the object’s moment of inertia.
Compare the resultant values from steps 2 and 3, and calculate the % error.
Questions:
Assuming that a person releases both a solid cylinder and solid sphere (with the same mass and radius) from rest at location A, which object do you expect will reach location B first?
If this experiment does not give you mass of the rolling object (solid cylinder/sphere), are you still able to calculate the % error of the moment inertia?
Based on the experimental data in the video, can you calculate the object’s translational acceleration and angular acceleration?
