Rigid bodies and rotational dynamics
| English | 中文 | Pinyin |
|---|---|---|
| torque/tɔːk/ | 力矩 | lì jǔ |
| moment of inertia/ˈməʊmənt ɒv ɪˈnɜːʃə/ | 转动惯量 | zhuǎn dòng guàn liàng |
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.
- Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.
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?
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.
Match each technical term to its precise meaning.
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.
- 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?
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.
Work from known quantities
- State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
- 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.
A 12 N force acts perpendicularly 0.25 m from the pivot. Find torque. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.
A 12 N force acts perpendicularly 0.25 m from the pivot. Find torque.
The result is 3 N m. 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.
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.
- Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.
Moment of inertia depends only on total mass, never its distribution. This claim is false: 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.
Rigid bodies and rotational dynamics: 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.
Moment of inertia depends only on total mass, never its distribution.
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.
Turning effect about an axis: write the technical term.
torque means Turning effect about an axis.