Motion And Gravity

Question 1

Define 1 radian

Answer 1

The angle subtended at the centre of a circle with an arc length equal to the radius.

Question 2

Length of arc (s) =

Answer 2

S = r ✖️theta

Length of arc = radius x angular displacement

Question 3

Speed of circular motion =

Answer 3

Speed = angular velocity x radius (v = wr)

Question 4

Angular velocity (w) =

Answer 4

Angular velocity = angular displacement / time

Question 5

Acceleration (a) of circular motion =

Answer 5

a = Angular velocity x speed
(a = wv)
a = speed squared ➗radius
(a = v^2 / r)

Question 6

State Newton’s law of gravitation

Answer 6

Any 2 point masses attract each other with a force directly proportional to the product of their masses, and indirectly proportional to the square of their separation. (F = GMm / r^2)

Question 7

Define gravitational field strength (and g = )

Answer 7

The gravitational force exerted per unit mass on a small object. (g = F/m ; g = Gm/r^2)

Question 8

Define gravitational potential (omega)

Answer 8

The work done per unit mass in bringing a mass from infinity to a point. (= -GMm / r)

Question 9

Kinetic energy in a gravitational field

Answer 9

k.e. = GMm/2r (from F = mvv/r = GMm/rr and k.e. = 0.5mvv)

Question 10

Velocity of an orbiting object (v) =

Answer 10

V^2 = GM/r

Question 11

The orbital period (T) =

Answer 11

T^2 = (4pi^2/GM)r^3

Question 12

Define an oscillation

Answer 12

The repeated movement of an object back and forth on either side of an equilibrium position

Question 13

Define free oscillations

Answer 13

The direct displacement of an object, causing it to oscillate at its natural frequency.

Question 14

Define forced oscillations

Answer 14

Objects are forced to vibrate/oscillate at a forced frequency, due to vibrations from a secondary source.

Question 15

Define the phase of an oscillating particle

Answer 15

The point that an oscillating particle has reached within 1 complete cycle.

Question 16

Define simple harmonic motion

Answer 16

The motion of an oscillator in which acceleration is directly proportional to displacement, but in the opposite direction.

Question 17

State the requirements for simple harmonic motion (s.h.m.)

Answer 17

1. A mass that oscillates
2. A position where the mass is in equilibrium
3. The presence of a restoring force which brings the mass back to a rest position (force is directly proportional to displacement, but in the opposite direction

Question 18

Angular frequency (w) =

Answer 18

W = 2pif

Question 19

State the defining equation of s.h.m. (a = )

Answer 19

a = -w^2 x

Question 20

Define damping

Answer 20

When the amplitude of oscillations decays exponentially over time, due to the effect of external forces.

Question 21

Define critical damping

Answer 21

The minimum amount of damping required to return an oscillator to its equilibrium position without oscillating (so oscillations die out immediately).

Question 22

Define resonance

Answer 22

When an oscillating system is forced to vibrate at its natural frequency, resulting in the maximum possible amplitude.

Question 23

State the characteristics of resonance

Answer 23

1. Natural frequency = driving frequency
2. Maximum amplitude
3. Absorbs the greatest possible energy from driver