Rigid bodies and rotational dynamics
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| torque/tɔːk/ | mô-men lực |
| moment of inertia/ˈməʊmənt ɒv ɪˈnɜːʃə/ | mô-men quán tính |
What would explain this observation?
- A door is easier to open when pushed near its outer edge. Force size alone does not determine the turning effect.
Build the model
- Torque 力矩 depends on force and perpendicular distance from the axis.
- Moment of inertia 转动惯量 describes resistance to angular acceleration and depends on mass distribution about a stated axis.
- torque: Turning effect about an axis.
- moment of inertia: Resistance to angular acceleration about a specified axis.
What increases torque for the same perpendicular force?
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
Torque = force x perpendicular distance from the axis, so for the same force a larger perpendicular lever arm gives a larger torque. This is why a longer spanner loosens a tight nut more easily.
Match each technical term to its precise meaning.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- For a rigid body about a fixed axis, net torque equals moment of inertia multiplied by angular acceleration.
- Rotational kinetic energy depends on angular speed squared.
- Angular momentum is conserved when net external torque is zero.
In the lab: Draw the pivot, force direction and perpendicular lever arm. Do not use the sloping distance from pivot to force point unless it is perpendicular to the force. For experiments, keep rotating parts guarded and loads secure.
Which two habits make the investigation or model in this case more defensible?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- Known: a 10 N perpendicular force acts 0.30 m from an axis.
- Torque = force × perpendicular distance = 10×0.30 = 3.0 N m.
- If moment of inertia is 0.60 kg square metres, angular acceleration = torque/inertia = 3.0/0.60 = 5.0 radians per second squared.
Your turn: A 12 N force acts perpendicularly 0.25 m from the pivot. Find torque.
A 12 N force acts perpendicularly 0.25 m from the pivot. Find torque.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
The result is 3 N m. Known: force 12 N perpendicular to a lever arm of 0.25 m. Use torque = force x perpendicular distance. Torque = 12 x 0.25 = 3.0 N m. A force through the pivot would give zero torque however large it was.
Check the conclusion and its limits
- Torque has unit N m but is a turning effect, not an energy store.
- Moment of inertia changes if the same mass moves farther from the axis.
Not true: Moment of inertia depends only on total mass, never its distribution. Moment of inertia depends on how mass is distributed relative to the axis: the same total mass farther from the axis gives a larger moment of inertia. That is why a skater spinning with arms extended slows when the arms are pulled in.
- Torque depends on force and perpendicular distance from the axis.
- For a rigid body about a fixed axis, net torque equals moment of inertia multiplied by angular acceleration.
- Watch for: torque has unit N m but is a turning effect, not an energy store.
Write from a torque of 8 newton metres
- A 20 N force acts perpendicularly 0.40 m from the pivot.
- Find the torque. Moment of inertia depends on how mass is distributed.
Moment of inertia depends on how mass is distributed relative to the axis: the same total mass farther from the axis gives a larger moment of inertia.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
True. Moment of inertia depends on how mass is distributed relative to the axis: the same total mass farther from the axis gives a larger moment of inertia. That is why a skater spinning with arms extended slows when the arms are pulled in.
Turning effect about an axis: write the technical term.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
torque means Turning effect about an axis.
A 20 N force acts perpendicularly 0.40 m from the pivot. What is the torque, and why does moment of inertia not depend only on total mass?
Torque is force times the perpendicular distance from the pivot. Mass closer to the axis contributes less to the moment of inertia.
What is the torque?
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
20 times 0.40 is 8 newton metres. Other options — 3 newton metres (the lesson force of 12 N at 0.25 m); 20 N (the force).