Worksheet on Circular Motion

1. Worksheet Motion in a circle 1
1. Convert the following angles into radians.
(a) 30° (b) 210° (c) 0.05° [3]
2. Convert the following angles from radians
into degrees.
(a) 1.0 rad (b) 4.0 rad (c) 0.15 rad [3]
3. A toy train moves round a circular track of
radius 0.50 m.
(a) How many radians has the train turned
through in moving 1.5 m along the track?
(b) What is this angle in degrees? [2]
4. An object moving in a circle at constant
speed rotates at 15 revolutions per minute.
Calculate the angular speed in radian per
second. (TAP) [1]
5. A rotating restaurant.
A high tower has a rotating restaurant that
moves slowly round in a circle while the
diners are eating. The restaurant is designed
to give a full 360° view of the sky line in the
two hours normally taken by diners.
(a) Calculate the angular speed in radians per
second.
(b) The diners are sitting at 20 m from the
central axis of the tower. Calculate their
speed in metres per second. Do you think
they will be aware of their movement relative
to the outside? (TAP) [3]
6. The minute hand of a watch is 5.0 cm
long. Calculate
(a) Its frequency,
(b) Its angular speed,
c) The speed of the free end.
7. The Earth takes one year to orbit the Sun
along a path of radius 1.5 x 1011
m.
Calculate
(a) The frequency of the Earth’s orbit,
(b) The Earth’s angular speed,
(c) The linear speed at which the Earth is
moving.
8. The blades on a propeller make 50
revolutions per second. The diameter of the
circle the blades describe is 4 m. Find
(a) The angular speed,
(b) The linear speed of the tip of the blade,
(c) The centripetal acceleration of the tip of
the blade,
(d) How would the acceleration vary from the
centre of the blades to the tip? [4]
10. A conical pendulum consists of a bob of
mass 90.50 kg attached to a string of length
1.0 m. The bob rotates in a horizontal circle
such that the angle the string makes with the
vertical is 30̊. Calculate
(a) The period of the motion,
(b) The tension in the string.
Assume g=10 m s-2
(LR)
11. A cyclist is turning a corner on a flat
ground. If the mass is 80 kg, the speed is
20 m s-1
, and the radius of curvature is 15 m,
what is the angle of inclination from the
vertical? [4]
12. A car of mass 1000 kg travels over a
humpback bridge of radius of curvature 50 m
at a constant speed of 15 m s-1
. Calculate
the magnitude and direction of the force
exerted by the car on the road when it is at
the top of the bridge.
Assume g=10 m s-2
(LR)
13.
A lump of clay of mass 300 g is placed close
to the edge of a spinning turntable. The
centre of mass of the lump of clay travels in a
circle of radius 12 cm.
(a) The lump of clay takes 1.6 s to complete
one revolution.
(i) Calculate the rotational speed of the clay.
(ii) Calculate the frictional force between the
clay and the turntable.
(b) The maximum magnitude of the frictional
force F between the clay and the turntable is
70% of the weight of the clay.
The speed of rotation of clay is slowly
increased. Determine the speed of the clay
when it just starts to slip off the turntable.
(PC) [6]

2. Worksheet Motion in a circle 2
14. A roller coaster has a vertical loop of
radius 12 m, and the speed of the cars round
the loop is 14 m s-1
. For a passenger of mass
60 kg, calculate
(a) The period of rotation,
(b) The contact force on at the top, bottom,
and sides of the loop.
(c) At which point in the loop does the
passenger feel the heaviest?
(d) What is the minimum speed for the roller
coaster for the passenger to remain in his
seat? (g = 10 m s-2
) [10]
15. A bucket of water is swung in a vertical
circle of radius 1.5 m. What must be the
minimum speed of the bucket at the highest
point of the circle if the water is to stay in the
bucket throughout the motion?
(g = 10 m s-2
) [2]
16. X
P
h
Y Z
The diagram shows a toy runway. After
release from a point such as X, a small model
car runs down the slope, ‘loops the loop’, and
travels on towards Z. The radius of the loop
is 0.25 m.
(i) Ignoring the effect of friction outline the
energy changes as the model moves from X
to Z.
(ii) What is the minimum speed with which
the car must pass point P at the top of the
loop if it is to remain in contact with the
runway?
(iii) What is the minimum value of h which
allows the speed calculated in (ii) to be
achieved?
The effect of friction can again be ignored.
(Assume g = 10 m s-2
). (NP) [7]
17. An elastic cord has an unextended length
of 13.0 cm. One end of the cord is attached to
a fixed point C. A small mass of weight 5.0 N
is hung from the free end of the cord. The
cord extends to a length of 14.8 cm, as
shown in Fig. 1.1.
The cord and mass are now made to rotate at
constant angular speed ω in a vertical plane
about point C. When the cord is vertical and
above C, its length is the unextended length
of 13.0 cm, as shown in Fig. 1.2.
(i) Show that the angular speed ω of the cord
and mass is 8.7 rad s–1
. [2]
(ii) The cord and mass rotate so that the cord
is vertically below C, as shown in Fig. 1.3.
Calculate the length L of the cord, assuming it
obeys Hooke’s law. [4]
(N07)