Torque, Moment of Inertia and Rotation About a Fixed Axis

Name: Torque, Moment of Inertia and Rotation About a Fixed Axis
Author: StemPy Lab

You push a door near its hinge, and then near its handle. The same force has a very different effect. In this course we define the vector product and the torque of a force, we find the moment of inertia of bodies of different shapes, and we write the law of rotation, torque equals moment of inertia times angular acceleration, to solve problems on pulleys, wheels and swinging rods.

3 lessons, about 1 h 10 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The vector product and the torque of a force
The vector product $\vec{A} \times \vec{B}$ has size $AB\sin\theta$ and points at right angles to both, by the right-hand rule; $\vec{A} \times \vec{B} = -\vec{B} \times \vec{A}$ . The torque of a force about a point is $\vec{\tau} = \vec{r} \times \vec{F}$ , of size $rF\sin\theta$ : the force times its moment arm, the perpendicular distance from the point to the force's line.
1 simulation2 practice questions1 Python program4 problems1 question set
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Lesson 2about 25 min
Moment of inertia and the two theorems on axes
The moment of inertia $I = \sum m_ir_i^2$ measures how hard a body is to set turning about an axis; it depends on the mass and on how far it lies from that axis. Standard values: ring $MR^2$ , disc $\tfrac12 MR^2$ , rod about its middle $\tfrac{1}{12}ML^2$ , solid sphere $\tfrac25 MR^2$ . Parallel axes: $I = I_{cm} + Md^2$ . Perpendicular axes (flat bodies): $I_z = I_x + I_y$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 20 min
Dynamics of rotation about a fixed axis
For rotation about a fixed axis, Newton's second law becomes $\tau = I\alpha$ : the net torque equals the moment of inertia times the angular acceleration. A turning body has kinetic energy $\tfrac12 I\omega^2$ ; a torque does work $\tau\theta$ and delivers power $\tau\omega$ . Problems with ropes on wheels join $\tau = I\alpha$ for the wheel with $F = ma$ for the load, through $a = \alpha R$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Torque, Moment of Inertia and Rotation: Practice Paper

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Torque, Moment of Inertia and Rotation About a Fixed Axis

Course outline (3 lessons)

The vector product and the torque of a force

Moment of inertia and the two theorems on axes

Dynamics of rotation about a fixed axis

Test Your Learning

Your teacher

Discussion (0)