A body circling at constant speed always feels centripetal force aimed at the centre, and at 4 m/s in a radius-2 m circle the centripetal acceleration comes out as 8 m/s², so this IB sheet starts from the core turning requirement. The key goes on to give 18 N for a force and F/4 when distance doubles.
Key Takeaways
Centripetal force points towards the centre for uniform circular motion (Q1).
At 4 m/s and radius 2 m the centripetal acceleration is 8 m/s² (Q2).
The key records a centripetal force of 18 N.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.For an object moving in a circle at constant speed, the centripetal force is directed
(a) away from the centre(b) towards the centre(c) tangentially in the direction of motion(d) vertically upward
2.An object moves at 4 m/s in a circle of radius 2 m. Its centripetal acceleration is
(a) 2 m/s²(b) 8 m/s²(c) 16 m/s²(d) 32 m/s²
3.A 2 kg mass moves at 3 m/s in a circle of radius 1 m. The centripetal force is
(a) 6 N(b) 9 N(c) 18 N(d) 27 N
4.The gravitational field strength at the surface of the Earth is approximately
5.The orbital period of a satellite increases with orbital radius because a larger radius gives
(a) a larger orbital speed(b) a longer path and a smaller orbital speed(c) the same orbital speed(d) a shorter path
6.Two masses attract each other with force F. If the distance between them is doubled, the force becomes
(a) F/2(b) F/4(c) 2F(d) 4F
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State the direction of the centripetal force acting on an object moving in uniform circular motion.
8.Explain why the centripetal force does no work on an object moving in a circle at constant speed.
9.State the equation for the centripetal acceleration of an object moving at speed v on a circular path of radius r.
10.State Newton's law of universal gravitation.
11.Explain what is meant by a geostationary satellite.
12.State the value of the gravitational field strength at the surface of the Earth.
13.Explain why an astronaut in an orbiting spacecraft appears to be weightless.
14.State the factors that determine the gravitational force between two point masses.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Using a = v² ÷ r, calculate the centripetal acceleration of a car travelling at 20 m/s around a bend of radius 100 m.
16.Using F = mv² ÷ r, calculate the tension in a string when a 0.5 kg stone moves at 10 m/s on a circle of radius 1 m.
17.Using F = Gm₁m₂ ÷ r² with G = 6.67 × 10⁻¹¹ N m²/kg², calculate the gravitational force between two 1 kg masses separated by 1 m.
18.Using g = GM ÷ R² with G = 6.67 × 10⁻¹¹ N m²/kg², M = 6.0 × 10²⁴ kg and R = 6.4 × 10⁶ m, calculate the gravitational field strength at the surface of the Earth.
19.Using v = √(GM ÷ r) with G = 6.67 × 10⁻¹¹ N m²/kg² and M = 6.0 × 10²⁴ kg, calculate the orbital speed of a satellite at a radius of 7.0 × 10⁶ m.
20.Using F = mv² ÷ r, calculate the centripetal force on a 0.8 kg ball moving at 5 m/s on a horizontal circle of radius 2 m.
Answer Key
1. b) towards the centre
2. b) 8 m/s²
3. c) 18 N
4. b) 9.8 N/kg
5. b) a longer path and a smaller orbital speed
6. b) F/4
7. Refer to solution guide.
8. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
Where is centripetal force directed?
Towards the centre, option (b) in this worksheet (Q1).
What is the centripetal acceleration at 4 m/s in a 2 m circle?
8 m/s², option (b) in this worksheet (Q2).
What happens to the gravitational force when distance doubles?
It falls to F/4, from the answer key on this page.
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