Unit 5 check
Unit 5 check: Torque and Rotational Dynamics
10 questions from 6 lessons in Unit 5. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.
Question 1 · from 5.1 · Calculate
You face a combination lock and take counterclockwise as positive. You turn its dial 2.5 revolutions clockwise. What is the dial's angular displacement, in radians? Include the sign, and give your answer to the nearest 0.01 rad.
Question 2 · from 5.2 · Sketch the graph
A helicopter's main rotor turns at a steady 40 rad/s. Sketch the linear speed of points on the rotor against their distance from the axis of rotation, along a line from the axis out to the tip of one blade, 5.0 m away. The first point is fixed at 0.
One shape that fits
Drag a point up or down, or tap it and use the arrow keys. The shape is checked, and the graph must pass through the values the question gives.
Question 3 · from 5.3 · Match
A light rod 0.60 m long turns about a pin through one end. Each force listed is 60 N and is exerted in the plane the rod turns in. Tap a force, then the lever arm it has about the pin.
Question 4 · from 5.4 · Match
A uniform rod of mass 2.0 kg and length 1.20 m has a rotational inertia of 0.24 kg·m² about an axis through its center, perpendicular to the rod. Every axis listed is parallel to that one. Tap an axis, then the rod's rotational inertia about it.
Setup for question 5
A new situation, where one support pulls instead of pushing. A uniform diving board, 3.0 m long with a mass of 20 kg, is held at its back end by a bolt and rests on a support 1.0 m in front of the bolt. A 55 kg diver stands at the front end, and the board is level and at rest. Look at the board from the side with the bolt on your left, and take counterclockwise as positive.
Question 5 · from 5.5 · Decide and justify
A uniform diving board is held at its back end by a bolt and rests on a support a little in front of the bolt. A diver stands at the front end, and the board is level and at rest. Seen from the side with the bolt on your left, does the bolt push the board up or pull it down?
Which reason supports your answer?
Setup for question 6
An engineering class tests four flywheels on one bench. Each turns on its own fixed axle and starts from rest. A motor exerts a constant counterclockwise torque on each one, as seen from the front, and friction at the axle exerts a constant clockwise torque against it while it turns.
| Flywheel | Rotational inertia (kg·m²) | Motor torque (N·m) | Friction torque (N·m) |
|---|---|---|---|
| P | 0.80 | 9.6 | 1.0 |
| Q | 0.20 | 3.2 | 1.4 |
| R | 0.40 | 6.0 | 0.8 |
| S | 0.60 | 10.0 | 4.0 |
Question 6 · from 5.6 · Calculate
Using the table of four flywheels, take counterclockwise as positive. What is flywheel Q's angular acceleration while its motor runs? Give your answer to the nearest 0.1 rad/s².
Question 7 · from 5.1 · Sort it
Each card names a system and the rotation a question is about. Tap a card, then decide whether the system can be treated as a single object for that question or must be described as a rigid system turning about its axis.
Treat it as a single object
Describe a rigid system's rotation
Question 8 · from 5.2 · Fill the statement
A circular saw is switched on, and its blade speeds up with a constant angular acceleration. Point P on the blade is 0.040 m from the axle, and point Q is 0.080 m from it. Tap a blank, then an answer.
P and Q have the same . Q's tangential acceleration is P's. Each point's tangential acceleration points .
Question 9 · from 5.3 · Sort it
A board is pinned at its left end so it can turn about the pin, and at this instant it lies level. You see it from the side, with the pin on your left. Tap each force on the board, then what it does about the pin.
Tends to turn it counterclockwise
Tends to turn it clockwise
No torque about the pin
Setup for question 10
A new situation, with more than two objects. A crop-spraying drone hovers over a field and turns in place to face a new row, spinning about a vertical axis through its center. Its heavy parts all lie in one level plane, and for this question each can be treated as a point. Work out its rotational inertia, then practice with objects on a light rod.
Question 10 · from 5.4 · Calculate
A crop-spraying drone hovers and turns in place about a vertical axis through its center. Its four motors, 2.5 kg each, sit at the ends of light arms, each 1.2 m from the axis. A 4.0 kg spray pump is mounted 0.50 m from the axis. All of these parts lie in one level plane. Treat each part as a point and the arms as massless. What is the drone's rotational inertia about that axis? Give your answer to the nearest 0.1 kg·m².
0 of 10 answered.