Why shape sets spin resistance

Science · Forces & Motion · ages 20-21

Name ______________________ Date ____________

The same body can have different moments of inertia about different axes.
Circle one: True False
Moment of inertia weights each bit of mass by which power of its distance from the axis?
- Distance to the first power
- Distance squared
- Distance cubed
For equal mass and radius, which shape has the largest moment of inertia?
- Solid disc
- Thin rod through its centre
- Thin hoop, mass at rim
A rod has centre of mass value 1 and mass 3. What does the parallel-axis theorem give about an axis 1 away?
- 1 plus 3 times 1 squared, which is 4
- 1 times 3 times 1, which is 3
- 1 minus 3, which is negative 2
A flywheel has I equal to 2 and spins with omega 3. What is its rotational kinetic energy?
Answer: ______________
Shifting the axis away from the centre of mass always lowers the moment of inertia.
Circle one: True False
A hoop of mass 2 and radius 3 has I equal to M R squared. What is I?
Answer: ______________
A student computes I by adding mass times distance (not squared) and finds the hoop equals the disc. What went wrong?
- Nothing, hoops and discs match
- Distance must be squared
- The integral should divide by distance

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · Mass sits differently around each axis, so the integral gives different values.
Distance squared · The integral sums mass times distance squared.
Thin hoop, mass at rim · The hoop keeps every bit at the full radius, farthest from the axis.
1 plus 3 times 1 squared, which is 4 · Add M times the squared shift to the centre value.
9 · Energy is half I omega squared.
False · Every shift adds a positive correction, so I only grows.
18 · All hoop mass sits at the rim, so multiply mass by radius squared.
Distance must be squared · Without the square, rim mass loses the extra weight that decides the ranking.