AQA Physics A-level Year 2
3.6 3.6.1
Further mechanics and thermal physics Periodic motion
3.6.1.1 Circular motion Angular measure You have previously studied the motion of objects which move in a straight line. You have used the equations of linear motion to describe such movement in terms of the time taken, t, the displacement, s, the acceleration, a, and the initial and final velocities, u and v. When an object moves in a circular path, the displacement may not be important, since after each full circle the displacement is zero. It is often more useful to consider the total angle, u, that has been turned through. The SI unit used to measure angles is the radian. The radian is defined using a circle. The angle in radians, u, at the centre of a circle is the ratio of the arc length, s, to the radius of the arc, r:
( in radians)
arcc length ar radi dius of arc dius ar
s r
Definition One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. Fig 1 When the arc length is equal to the radius, the angle u is equal to one radian.
r
s
θ
s θ= r
r
If we consider a full circle, the arc length is the circumference, s = 2pr, so: 2 r ( radians) 2 r In other words, there are 2p radians in a full circle. As there are 360° in a full circle, we can use this to convert radians to degrees (see Table 1). Table 1 Conversions between radians and degrees 4
89532_P001_124.indd 4
Radians
Degrees
2p
360°
1
360/2p = 57.3°
2p/360 = 0.017
1°
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