1© Manhattan Press (H.K.) Ltd. Weightlessness Artificial gravity Artificial gravity 5.7 Weightlessness and artificial gravity

2 © Manhattan Press (H.K.) Ltd. Weightlessness 5.7 Weightlessness and artificial gravity (SB p. 191) Feels weightless in spaceship - moving with uniform circular motion around earth in space centripetal force - by total weight of spaceship and astronaut

3 © Manhattan Press (H.K.) Ltd. Weightlessness 5.7 Weightlessness and artificial gravity (SB p. 191) For whole system For astronaut only No reaction on astronaut (weightless)

4 © Manhattan Press (H.K.) Ltd. Artificial gravity 5.7 Weightlessness and artificial gravity (SB p. 192) Artificial gravity - help astronauts to stay long time in space 1. Wheel-like space station 2. Two rotating space capsules with central connecting axis

5 © Manhattan Press (H.K.) Ltd. 5.1 Angular velocity and linear velocity 5.7 Weightlessness and artificial gravity (SB p. 193) 1.For a mass moves in a circle from A to B, the radius r subtends an angle θ at the centre of the circle. The angle θ can be measured in radians or degrees. It is known as angular displacement: where s is the length of the arc.

6 © Manhattan Press (H.K.) Ltd. 5.1 Angular velocity and linear velocity 5.7 Weightlessness and artificial gravity (SB p. 193) 2. The angular velocity (  ) of the mass is defined as the rate of change of angular displacement. where t is the time interval. The unit of  is radians per second (rad s –1 ) or revolutions per second (rev s –1 ). 3. The linear velocity of the mass is: v = r 

7 © Manhattan Press (H.K.) Ltd. 5.2 Centripetal acceleration and force 5.7 Weightlessness and artificial gravity (SB p. 193) 4. An object in uniform circular motion experiences centripetal acceleration which is the acceleration directed towards the centre of the circle. 5. Centripetal acceleration (a) is:

8 © Manhattan Press (H.K.) Ltd. 5.2 Centripetal acceleration and force 5.7 Weightlessness and artificial gravity (SB p. 193) 6. Centripetal force (F c ) is: 7. For a uniform circular motion: Centripetal force is always perpendicular to the motion of the body. It does no work on the body and the kinetic energy of the body remains unchanged.

9 © Manhattan Press (H.K.) Ltd. 5.3 Vehicles rounding bends 5.7 Weightlessness and artificial gravity (SB p. 193) 8. When a vehicle turns around a corner, the sideway friction between the tyres and the ground provides the centripetal force that enables the vehicle to follow the curved track. The maximum speed of the vehicle is independent of its mass. 9. When a vehicle turns around a banked bend of angle θ, the centripetal force is provided by the components of the normal reactions towards the centre of the curve bend.

10 © Manhattan Press (H.K.) Ltd. 5.4 Aircraft turning in flight 5.7 Weightlessness and artificial gravity (SB p. 193) 10. In a level flight, an aircraft experiences a lifting force (L), which is perpendicular to the surface of its wings. It balances the weight of the aircraft (mg). 11. To turn around, the aircraft must tilt an angle θ, so that the horizontal component of the lifting force provides the necessary centripetal force, and its vertical component balances the weight of the aircraft. The tilting angle depends only on the aircraft’s speed and the radius of the turn.

11 © Manhattan Press (H.K.) Ltd. 5.5 Looping the loop (Motion in a vertical circle) 12. Consider a particle of mass m revolving at a constant speed v in a vertical circle of radius r by means of a string. The tension at the bottom is a maximum and that at the top is a minimum. 5.7 Weightlessness and artificial gravity (SB p. 193)

12 © Manhattan Press (H.K.) Ltd. 5.6 Centrifuge 13. A centrifuge consists of microcentrifugal tubes which are freely hinged at a pivot and rotated at a high angular speed  in a horizontal circle. It is used to separate suspension particles from the liquid or liquids of different densities. 5.7 Weightlessness and artificial gravity (SB p. 193)

13 © Manhattan Press (H.K.) Ltd. 5.7 Weightlessness and artificial gravity 14. An astronaut feels weightless in a spaceship which is moving with uniform circular motion around the earth in space. 5.7 Weightlessness and artificial gravity (SB p. 193)

14 © Manhattan Press (H.K.) Ltd. 5.7 Weightlessness and artificial gravity (SB p. 194)

15 © Manhattan Press (H.K.) Ltd. End