LAB 8 - Centripetal Acceleration vs. Angular Frequency
Tony Wu, Leslie Zhao, Isaiah Hernandez
September 28, 2016
Experimental Procedure: We attached a 200 g mass to a string of length 19 cm and set the voltage to 6.1 volts. We let the disk speed up until it was running at a roughly a constant speed. We took note of how many seconds it took for 10 full rotations of the disk. We then recorded the force reading. We repeated this process with different masses, lengths of string, and different voltages.
Data and Calculations:
Conclusions: The conclusions came out as it would have intuitively. The equation for centripetal force is:
Fcentripetal = m*r*ω2
An increase in mass means a greater centripetal force. A decrease in mass means a smaller force. This makes sense as force is mass times acceleration. An increase in string length, or radius leads to an increase in force, as is verified in our data above. An increase in voltage, leading to a larger omega value, also leads to a greater force.
Lab Goal: To determine the relationship between centripetal acceleration and angular speed.
Theory/Introduction: Centripetal acceleration is the acceleration of an object towards the center of a circular path. Centripetal means "center seeking". An object traveling in a circular path can accelerate even if it's moving at a constant speed. Acceleration also means change in direction of the velocity. Therefore, an object traveling in a circle with constantly changing velocity has its acceleration towards the center at any moment.
Apparatus: Large heavy rotating wooden disk, powered by a motor with variable voltages. The disk rotates at higher velocities as the voltage is increased. At the center of the disk is a force gauge with a string attached to a mass. The force gauge reads the tension in the string which is equal to the centripetal force. The force varies depending on the size of the mass, the length of the string, and the voltage that the disk rotates.
Theory/Introduction: Centripetal acceleration is the acceleration of an object towards the center of a circular path. Centripetal means "center seeking". An object traveling in a circular path can accelerate even if it's moving at a constant speed. Acceleration also means change in direction of the velocity. Therefore, an object traveling in a circle with constantly changing velocity has its acceleration towards the center at any moment.
Apparatus: Large heavy rotating wooden disk, powered by a motor with variable voltages. The disk rotates at higher velocities as the voltage is increased. At the center of the disk is a force gauge with a string attached to a mass. The force gauge reads the tension in the string which is equal to the centripetal force. The force varies depending on the size of the mass, the length of the string, and the voltage that the disk rotates.
Experimental Procedure: We attached a 200 g mass to a string of length 19 cm and set the voltage to 6.1 volts. We let the disk speed up until it was running at a roughly a constant speed. We took note of how many seconds it took for 10 full rotations of the disk. We then recorded the force reading. We repeated this process with different masses, lengths of string, and different voltages.
Data and Calculations:
Recorded Data with Varying Mass, String Length, and Voltage
These graphs show how a change in mass, radius, or omega affects the centripetal force.
Fcentripetal = m*r*ω2
An increase in mass means a greater centripetal force. A decrease in mass means a smaller force. This makes sense as force is mass times acceleration. An increase in string length, or radius leads to an increase in force, as is verified in our data above. An increase in voltage, leading to a larger omega value, also leads to a greater force.
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