THE PRACTICE STUDIO
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PRACTICE / Moment of inertia
One axis for the whole rotor
A uniform rod of mass 3 kg and length 2 m rotates about a fixed axis through one end, perpendicular to the rod. A 1 kg point mass is attached 1 m from that axis. The net external torque about the axis is 10 N·m.
What is the instantaneous angular acceleration?
Organize the givens & assumptions
- Rod: 3 kg, 2 m
- Point mass: 1 kg at 1 m
- Net torque: 10 N·m
Rigid attachment; friction already included in the stated net torque; all moments use the same fixed axis.
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Problem: One axis for the whole rotor
A uniform rod of mass 3 kg and length 2 m rotates about a fixed axis through one end, perpendicular to the rod. A 1 kg point mass is attached 1 m from that axis. The net external torque about the axis is 10 N·m.
Question: What is the instantaneous angular acceleration?
Givens:
- Rod: 3 kg, 2 m
- Point mass: 1 kg at 1 m
- Net torque: 10 N·m
Assumptions: Rigid attachment; friction already included in the stated net torque; all moments use the same fixed axis.
Choices (LaTeX):
A. 2\ \mathrm{rad/s^2}
B. 5\ \mathrm{rad/s^2}
C. 2.5\ \mathrm{rad/s^2}
D. 1.25\ \mathrm{rad/s^2}
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
Inertia can be added only after every contribution refers to the same axis.
Shift the rod inertia
For a uniform rod, shifting its central axis by L/2 gives the end-axis inertia.
Include the attachment
Its small size is neglected, so only its distance to the axis enters.
Find the acceleration
The stated torque is already the resultant about this fixed axis.
The rod needs 8 N·m and the point contribution needs 2 N·m at this acceleration.
TRY THE IDEA AGAIN
Move the point mass to the pivot without changing the rod or torque. What is α?
YOUR LEARNING NOTE
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