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S6 Physics: Circular Motion and Gravitation – Error Revisit Practice (10 Questions)
S6 Physics: Circular Motion and Gravitation – Error Revisit Practice (10 Questions)
Ten items revisit the usual slips: converting between speed and period, why a change of direction is still an acceleration, the v squared over r formulas for centripetal acceleration and force, surface g from GM over R squared, orbital speed and period from the square root of GM over r, the 8-fold period for a 4-fold radius, and the two conceptual traps that centripetal force is not an extra force and that weightlessness is not the absence of gravity.
Quick answer 1. 0.785 m/s; 2. the direction of velocity keeps changing, so the acceleration points to the centre; 3. 18 m/s²; 4. 5 N; 5. about 9.81 m/s²; 6. about 7.5 km/s; 7. about 5.8×10^3 s, that is 97 minutes; 8. 8 times; 9. no, it is the resultant force; 10. no, gravity still acts and provides the centripetal force.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 20 minutes |
| Difficulty mix | Foundation 2 · Intermediate 3 · Challenge 3 · Error redo 2 |
| Chapter | Chapter: S6 Physics | Circular Motion and Gravitation: centripetal force, orbital speed and period |
| Level | S6 |
02 Questions (10 items)
- FoundationAn object moves in a circle of radius 0.5 m with a period of 4 s. What is its speed?
- FoundationIn uniform circular motion the speed does not change. Why is there still an acceleration?
- IntermediateAn object moves in a circle of radius 2 m at 6 m/s. What is its centripetal acceleration?
- IntermediateA 0.5 kg object moves at 4 m/s in a circle of radius 1.6 m. What centripetal force is needed?
- IntermediateGiven G = 6.67×10^-11, the mass of the Earth 5.97×10^24 kg and its radius 6.37×10^6 m, find g at the surface.
- ChallengeA satellite orbits at 7.0×10^6 m from the centre of the Earth. What is its orbital speed?
- ChallengeFor the same satellite, how long does one orbit take?
- ChallengeIf the orbital radius becomes 4 times larger, by what factor does the period change?
- Error redoIs centripetal force an extra, additional kind of force?
- Error redoAstronauts in a space station feel weightless. Is that because there is no gravity there?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 0.785 m/s. | Speed is circumference divided by period, so it rises with radius and falls with period. |
| 2 | Because the direction of the velocity keeps changing, giving a centripetal acceleration towards the centre. | Acceleration is the rate of change of the velocity vector, so a change of direction alone counts. |
| 3 | 18 m/s². | Centripetal acceleration is v squared over r, that is 36 divided by 2. |
| 4 | 5 N. | The centripetal force is m v squared over r, that is 0.5 times 16 divided by 1.6, directed to the centre. |
| 5 | About 9.81 m/s². | Surface g equals GM over R squared, so substituting the three values gives about 9.8. |
| 6 | About 7.5×10^3 m/s, that is 7.5 km/s. | Gravity supplies the centripetal force, so v is the square root of GM over r, and a larger r means a smaller speed. |
| 7 | About 5.8×10^3 s, that is roughly 97 minutes. | The period is the circumference 2 pi r divided by the speed v. |
| 8 | 8 times. | Because the square of the period is proportional to the cube of the radius, 4 to the power 1.5 gives 8. |
| 9 | No. It is the resultant force, supplied by gravity, tension, friction or a normal force. | A common slip is to draw an extra centripetal arrow on the free-body diagram instead of resolving the real forces along the radius. |
| 10 | No. Gravity still acts and provides the centripetal force, and the crew and station fall freely together so they press on nothing. | Weightlessness means no support force is felt, not that gravity has vanished, and g in orbit is only slightly less than at the surface. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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