This chapter is for Higher Level students only. By the end of this chapter, you should be able to:
H
} convert and use angles in radian format } describe circular motion in terms of tangential speed, linear speed and angular velocity
} derive linear speed and angular velocity
} understand and derive centripetal force and centripetal acceleration
} explain satellite motion and geostationary orbits with reference to Newton’s universal law of gravitation } derive Kepler’s third law.
Introduction
The notion of circular motion is one in which we can study the motion of particles, whether they be large vehicles turning or small electrons moving in a magnetic field. We will revisit the concept of circular motion in Topic 5 Electricity and Topic 6 Modern physics.
In this chapter, we will deal with circular motion from a classical sense of Newtonian mechanics. This is an area dealing with such things as velocity, acceleration and satellite behaviour. In order to introduce circular motion properly, we need to introduce a new unit used specifically for this type of movement. This unit is the radian.
Radians
One radian (1 rad) is the angle subtended from (made by) an arc that has a length equal to the radius.
This is the only part of the Leaving Certificate Physics course where you will need to be careful about using a different angle measurement. This unit is the radian (not degrees).
The circle in Fig. 8.1 has a radius length x. The angle θ between the two radii each side of the arc of length x is therefore 1 rad because the radius is equal to the arc length.
x
(rad) x
x (arc length)
FIG. 8.1 The angle q is 1 rad because the radius is equal to the arc length
