9. A satellite orbits the Earth at a height of 200 km above the Earth’s surface. Calculate the linear speed of the satellite and the period of the satellite’s orbit. (Mass of Earth, M = 6 × 1024 kg, Radius of Earth = 6.4 × 106 m, G = 6.7 × 10–11 N m2 kg–2)
Solution F = mv2
_____ r = GMm
(cancelling m
______ r2 ⇒ v2 = GM
____ r
___ r from both sides)
You may now complete Exercise 8D (page 81). CHAPTER 8 EXERCISE 8A
1. Convert the following measurements to degrees:
(i) 2 rad (iv) 2π
____ 6 rad
2. Convert the following measurements to radians:
(i) 45° (ii) 60° (iii) 180° (iv) 270° (ii) π rad (iii) 1
_ 4 π rad
3.
A circle has a radius of 20 cm. Find in radians the angle at the centre of a circle which is subtended by an arc of length:
(i) 15 cm (ii) 20 cm (iii) 5 cm
4. How many radians are there in a quarter circle?
5. A pendulum is 2.5 m in length and traces out an angle of 25°. Determine the length of arc that the pendulum travels through.
CHAPTER 8 EXERCISE 8B
1. If an object travelling in a circular path of radius 8 m has an angular velocity of 2 rad s–1, how long will it take for the object to travel a distance of 150 m?
2. If an object moving in a circular motion of radius 5 m, at a uniform velocity, is capable of travelling 100 m in 4 minutes, calculate:
(i) its angular velocity (ii) its linear speed.
3. What is the relationship between angular speed and linear speed?
4. A record turntable is rotating at 45 revolutions per minute. Calculate its angular velocity in rad s–1.
5. (i) Calculate the Earth’s linear speed.
(ii) At what angular speed does the Earth orbit the Sun? (1 year = 3.2 × 107 s)
6. An object on the circumference of a circle of radius 20 cm has a speed of 5 m s–1. Calculate its angular velocity.
