2006 Question 6
(i) Define velocity.
Velocity is the rate of change of displacement with respect to time.
(ii) Define angular velocity.
Angular velocity is the rate of change of angle with respect to time.
(iii) Derive the relationship between the velocity of a particle travelling in
uniform circular motion and its angular velocity.
θ = s /r
θ /t = s/rt
ω = v /r
v = ω r
(iv) A student swings a ball in a circle of radius 70 cm in the vertical plane as shown. The angular
velocity of the ball is 10 rad s–1. What is the velocity of the ball?
v = ω r = (10)(0.70) = 7.0 m s-1
(v) How long does the ball take to complete one revolution?
T= 2πr/v = 2π(0.70)/v = 0.63 s
(vi) Draw a diagram to show the forces acting on the ball when it is at position A.
Weight (W) downwards; reaction (R) upwards; force to left (due to friction or curled fingers)
(vii) The student releases the ball when is it at A, which is 130 cm above the ground, and the ball
travels vertically upwards. Calculate the maximum height, above the ground, the ball will
reach.
v2 = u2+ 2as 0 = (7)2 + 2(-9.8) s / s = 2.5(0) m max. height = 2.5 + 1.30 /
3.8 m
(viii) Calculate the time taken for the ball to hit the ground after its release from A.
s = ut + ½ at2
-1.30 = 7t – ½ (9.8)t2
t = 1.59 s
2006 Question 12 (a)
(i) Define pressure.
Pressure = Force divided by area.
(ii) Is pressure a vector quantity or a scalar quantity? Justify your answer.
It is a scalar because it has no direction.
(iii) State Boyle’s law.
Boyle’s Law states that pressure is inversely proportional to volume if temperature is constant.
(iv) A small bubble of gas rises from the bottom of a lake. The volume of the bubble increases
threefold when it reaches the surface of the lake where the atmospheric pressure is 1.01 ×
105 Pa. The temperature of the lake is 4 oC. Calculate the pressure at the bottom of the lake.
Pressure at bottom = 3 × pressure at top = 3.03 × 105 Pa
(v) Calculate the depth of the lake.
Pressure at bottom due to water = 2.02 × 105 Pa
P= hρg
h = P/ρg = 2.02 × 105 / (1.0 × 103)( 9.8 ) = 20.61 m
