Worksheet 2FA Pair work

Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1    Convert the following angles into radians.

a    30°                                                                                                                                  [1]

b    210°                                                                                                                                 [1]

c    0.05°                                                                                                                                [1]

2    Convert the following angles from radians into degrees.

a    1.0 rad                                                                                                                             [1]

b    4.0 rad                                                                                                                             [1]

c    0.15 rad                                                                                                                            [1]

3    The planet Mercury takes 88 days to orbit once round the Sun.
Calculate its angular displacement in radians during a time interval of:

a    44 days                                                                                                                            [1]

b    1 day.                                                                                                                               [1]

4    In each case below, state what provides the centripetal force on the object.

a    A car travels at a high speed round a sharp corner.                                                              [1]

b    A planet orbits the Sun.                                                                                                     [1]

c    An electron orbits the positive nucleus of an atom.                                                              [1]

d    Clothes spin round in the drum of a washing machine.                                                        [1]

5    The diagram shows a stone tied to the end of a length of string.
It is whirled round in a horizontal circle of radius 80 cm.

The stone has a mass of 90 g and it completes 10 revolutions in a time of 8.2 s.

a    Calculate:

i     the time taken for one revolution                                                                                  [1]

ii    the distance travelled by the stone during one revolution (this distance is equal to the circumference of the circle)                                                                                                                         [1]

iii   the speed of the stone as it travels in the circle                                                              [2]

iv   the centripetal acceleration of the stone                                                                        [3]

v    the centripetal force on the stone.                                                                                 [2]

b    What provides the centripetal force on the stone?                                                                [1]

c    What is the angle between the acceleration of the stone and its velocity?                              [1]

6    A car of mass 820 kg travels at a constant speed
of 32 m s⁻¹ along a banked track.
The track is banked at an angle of 20°
to the horizontal.

a    The net vertical force on the car is zero.
Use this to show that the contact force R on the car is 8.56 kN.                                            [2]

b    Use the answer from a to calculate the radius of the circle described by the car.                    [4]

7.   A stone of mass 120 g is fixed to one end of a light rigid rod.

The stone is whirled at a constant speed of 4.0 m s⁻¹ in a vertical circle of radius 80 cm.

Calculate the ratio:                                                                          [6]