Angular Motion

Question 1

linear motion vs angular motion

displacement = s (m)
initial velocity = u (ms-1)
final velocity = v (ms-1)
acceleration = a (ms-2)
time = t (s)

Answer 1

linear motion vs angular motion

angular displacement = w (rad)
initial angular velocity = w₀ (rad s-1)
final angular velocity = w (rad s-1)
angular acceleration = α ( rad s-2)
time = t (s)

Question 2

w = dθ / dt

Answer 2

w = angular velocity (rad s-1)
θ = angular displacement (rad)
t = time (s)

Question 3

w = v/r

Answer 3

w = angular velocty (rad s-1)
v = linear velocty (ms-1)
r = distance from axis of rotation (m)

Question 4

w = 2π/ T

Answer 4

w = angular velocity (rad s-1)
π = pi 
T = period of rotation (s)

Question 5

since frequency, f = 1/T this equation could also be stated as

w = 2πf

Answer 5

w = angular velocity (rad s-1)
π = pi
f = frequency (Hz)

Question 6

linear motion vs angular motion - equations

v = u + at
s = ut + 1/2at^2
v^2 = u^2 + 2as
s = 1/2 (u+v)t

Answer 6

linear motion vs angular motion - equations

w = w₀ + αt
θ = w₀t + 1/2αt^2
w^2 = w₀^2 + 2αθ
θ = 1/2(w₀ + w)t

Question 7

T = time/revolutions

Answer 7

T = period (s)

Question 8

θ = 2π x revolutions

Answer 8

θ = angular displacement (m)
π = pi

Question 9

Tangential Acceleration

aₜ = rα

of an object which is on a curved path

Answer 9

aₜ = tangential acceleration (ms-2)
r = radius (m)
α = angular acceleration (rad s-2)

Question 10

Centripetal Acceleration

aᵣ = v^2/r and aᵣ = w^2r

of an object moving in a circular path towards the centre of axis of rotation.

Answer 10

aᵣ = centripetal acceleration (ms-2)
r = radius (m)
v = linear velocity (ms-1)
w = angular velocity (rad s-1)

Question 11

The direction of the centripetal acceleration is ALWAYS towards

Answer 11

the centre of the circle
and
is at right angles to the tangential acceleration

Question 12

Centripetal Force

F = mv^2/r and F=mrw^2

Answer 12

F = Centripetal force (N)
m = mass (kg)
r = radius (m)
v = linear velocity (ms-1)
w = angular velocity (rad s-1)

Question 13

Centripetal force = mgtanθ

Plane Banking

Answer 13

W =mg is balanced by the lift of an aeroplane.
When it banks it is at an angle this provides an upwards component to balance the weight and a centripetal component causing the plane to turn.

Question 14

Conical Pendulum

\
|θ \ T
|___\
Tsinθ

Answer 14

Tcosθ = mv/r       divide the two
Tsinθ = mg          divide the two
tanθ = mv^2/r 
mv^2/r = F

tanθ = F/mg

F = Centripetal force
mg = W

Question 15

Centripetal radial or central force acting on an object is NECESSARY to

Answer 15

maintain circular motion and results in centripetal ACCELERATION of the object.

Question 16

tensions direction will be found on the

and weights direction will be found on the

Answer 16

tensions - on the string

weight on the object

Question 17

Why does an object travelling in a circular motion accelerate?

Answer 17

There is an unbalanced centripetal force acting on the object

Question 18

would an object lose contact with a track if the mass is reduced and it travels at the same speed as before?

Answer 18

the car will not lose contact with the track.
As a smaller centripetal force is supplied by a
smaller weight.

Question 19

To calculate the conical pendulum Tension, Weight or Fc you must

Answer 19

use Pythagoras’s theorem

Question 20

w = θ/t

Answer 20

when given revolutions per minute