Circular Motion for Physicists
Main Formulae
Key to symbols used

Linking angular velocity, angle turned and time:
T
Linking angular velocity and Period :
f 
Linking frequency and Period:

t
F = Centripetal Force (in N)
2
v = linear velocity (in m/s)

 = angular velocity (in radians/sec)
1
T
r = radius (in m)
v  r
Linking angular velocity, linear velocity and radius:
v2
Linking linear velocity, radius and inwards acceleration: a 
r
mv 2
r
Linking Centripetal Force, linear velocity and radius:
F
Linking Centripetal Force, angular velocity and radius:
F  mr 2
m = mass (in kg)
T = Period (in secs)
f = frequency (in Hertz)
 = angle turned in radians
a = inwards acceleration (in m/s2)
t = time (in secs)
Questions related to circular motion:
1) What angular velocity corresponds to a frequency of 50 Hertz?
2) A cyclist completes one lap of a circular track of 90 metre radius in a time of 40 secs. Calculate the
average speed in a) metres per second and b) km per hour.
3) An Earth satellite is orbiting the Earth in an approximately circular orbit whose radius may be taken
as 6000km. Calculate the steady speed of movement along the orbit. (Take g = 10 m/s 2) (Tip – the
centripetal force is the weight mg of the satellite – and the m’s will cancel out!!)
4) A planet P of mass m orbits the Sun S of mass M in a circular orbit of radius r as shown in Fig. 2.1.
Fig. 2.1
The speed of the planet in its orbit is v.
WorkFGDT 
(a) On Fig. 2.1, draw an arrow to represent the linear velocity of P. Label the arrow V. Draw a second arrow
representing the direction of the force acting on P. Label this arrow F.
[2]
(b) (i) Write down an expression, in terms of r and v, for the magnitude of the centripetal acceleration of P.
[1]
(ii) Write down an expression, in terms of m, r and v, for the magnitude of the force F acting on P.
[2]
(iii) Write down an expression, in terms of m, M, r and G, for the magnitude of the gravitational force exerted
by the Sun on the planet.
[1]
5) An aircraft flies with its wings tilted as shown in Fig. 2.2 in order to fly in a horizontal circle of radius r.
The aircraft has mass 4.00 x 104 kg and has a constant speed of 250 m/s.
Fig 2.2
With the aircraft flying in this way, two forces acting on the aircraft in the vertical plane are the force P acting
at an angle of 35o to the vertical and the weight W.
a)
b)
c)
d)
e)
State the vertical component of P for horizontal flight.
Calculate P
Calculate the horizontal component of P
Use F = ma to find the acceleration of the aircraft towards the centre of the circle
Calculate the radius r of the path of the aircraft’s flight.
WorkFGDT 