A solid steel disk undergoes a three-stage motion about its fixed axle
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A solid steel disk undergoes a three-stage motion about its fixed axle.
• Stage I (acceleration): Beginning from rest at t=0, the disk’s angular speed increases uniformly for 2.0s.
• Stage II (coasting): For the next 3.0s, the disk turns at the constant angular speed reached at the end of Stage I.
• Stage III (deceleration): During the final stage, the disk slows uniformly to rest in 2.0s.
The magnitude of the angular acceleration in Stage III is equal to that in Stage I.
Throughout the motion the positive direction is counterclockwise.
A student wants to represent the motion graphically.
(a) Sketch a qualitative graph of angular acceleration α(t) for the full 7.0s interval, clearly labeling values on the time axis and indicating the non-zero magnitudes relative to one another.
(b) On a separate set of axes, sketch a qualitative graph of angular velocity ω(t) over the same time interval. Clearly show key values and slopes but do not calculate numerical values.
(c) Explain how the requirement of continuity for ω and for angular displacement θ constrains the shapes of your two graphs at the boundaries between the three stages.