Engineers test a new rotating platform by recording simultaneous measurements of…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
Engineers test a new rotating platform by recording simultaneous measurements of angular speed ω and linear speed v for a marker fixed to the outer edge. The data collected at five different times are shown in the table.
Trial
ω (rad s⁻¹)
v (m s⁻¹)
1
0.80
0.66
2
1.20
0.99
3
1.60
1.33
4
2.00
1.66
5
2.40
2.01
Assume the platform maintains a single, constant radius during the tests and that the marker does not slip.
(a) Using the data, plot v (vertical axis) versus ω (horizontal axis) on appropriately scaled axes. Draw the best-fit straight line through the points.
(b) From your graph, determine the slope of the best-fit line and interpret its physical meaning in the context of the rotating platform.
(c) Use the slope to calculate the radius of the platform.
(d) Evaluate the consistency of the data with the assumption of a single constant radius. Support your answer with quantitative or graphical evidence.
(e) Predict the linear speed of the marker if the platform’s angular speed is increased to 3.00 rad s⁻¹, and state any assumptions made.