Angular velocity ω is the angle turned per unit time and centripetal acceleration is v²/r, so this Year 13 circular-motion sheet is built on how quickly an object swings through its circle. The key also records 4π rad s⁻¹ and that direction change is what keeps velocity changing.
Key Takeaways
Angular velocity is the angle turned per unit time (Q1).
Centripetal acceleration is v²/r (Q2).
Velocity changes in circular motion because its direction changes.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The angular velocity ω of an object is defined as...
(a) the angle turned per unit time(b) the distance moved per unit time(c) the number of revolutions per second(d) the speed divided by the radius squared
2.The centripetal acceleration of an object moving at speed v in a circle of radius r is...
(a) v/r(b) v²/r(c) rv²(d) r/v
3.The centripetal force on an object in circular motion always acts...
(a) away from the centre of the circle(b) towards the centre of the circle(c) along the direction of motion(d) tangentially to the circle
4.A mass on a string moves at 2 m s⁻¹ in a circle of radius 0.5 m. Its centripetal acceleration is...
(a) 4 m s⁻²(b) 1 m s⁻²(c) 8 m s⁻²(d) 2 m s⁻²
5.An object rotates at 2 revolutions per second. Using ω = 2πf, its angular velocity is...
(a) π rad s⁻¹(b) 2π rad s⁻¹(c) 4π rad s⁻¹(d) 8π rad s⁻¹
6.A body moves at constant speed in a circle. Which statement is correct?
(a) Its velocity is constant(b) Its velocity changes because its direction changes(c) Its acceleration is zero(d) No resultant force acts on it
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Define angular velocity and give its SI unit.
8.Define the radian.
9.State the relationship between linear speed v, angular velocity ω and radius r.
10.What force provides the centripetal force on a satellite orbiting the Earth?
11.Explain why a body moving at constant speed in a circle is accelerating.
12.Define centripetal force.
13.Write down the equations for centripetal force in terms of v and in terms of ω.
14.For a fixed radius, what happens to the required centripetal force if the speed is doubled?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A car travels round a circular track of radius 50 m at 20 m s⁻¹. Using a = v²/r, calculate the centripetal acceleration.
16.A 2 kg mass on a string moves at 4 m s⁻¹ in a circle of radius 0.5 m. Using F = mv²/r, calculate the tension in the string.
17.An object rotates on a turntable 0.2 m from the centre with a period of 2 s. Using ω = 2π/T, calculate the angular velocity and the linear speed v = rω.
18.A satellite orbits at a radius of 7×10⁶ m with a period of 6000 s. Using v = 2πr/T, calculate its orbital speed and its centripetal acceleration a = v²/r.
19.A pilot of mass 80 kg moves at 60 m s⁻¹ through the bottom of a vertical loop of radius 300 m. Using F = mg + mv²/r with g = 9.8 m s⁻², calculate the force exerted by the seat on the pilot.
20.A fairground ride rotates once every 4 s with riders at a radius of 3 m. Calculate the angular velocity using ω = 2π/T and the centripetal acceleration using a = rω².
Answer Key
1. a) the angle turned per unit time
2. b) v²/r
3. b) towards the centre of the circle
4. c) 8 m s⁻²
5. c) 4π rad s⁻¹
6. b) Its velocity changes because its direction changes
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End of Worksheet
People Also Ask
What is angular velocity ω?
The angle turned per unit time, option (a) in this worksheet (Q1).
What gives the centripetal acceleration?
v²/r, option (b) in this worksheet (Q2).
Why does velocity keep changing in circular motion?
Because its direction changes, from the answer key on this page.
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