A 140 g ball and a 220 g ball are connected by a 40-cm-long, massless, rigid rod

Question

A 140 g ball and a 220 g ball are connected by a 40-cm-long, massless, rigid rod. The balls rotate about their center of mass at 140 rpm. What Is the speed of the 140 g ball? Express your answer to two significant figures and include the appropriate units. A car tire is 65.0 cm in diameter. The car is traveling at a speed of 18.0 m/s. What is the tire's rotation frequency, in rpm? Express your answer to three significant figures and include the appropriate units. What is the speed of a point at the top edge of the tire? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

1) The position of the centre of mass of the system from the 140g ball
xcom   = m2 x d / m1 + m2
Where m1 and m2 are 220 and 140 grams respectively and d is the distance between the masses
xcom  = 220 x 40 / 220+140 = 24.44 cm
The 140 g mass is at a distance of ( 40 -24.44 )cm = 15.55 cm from the centre of mass
Thus r = 15.55 cm
The angular velocity is 140 rpm = 2 x 3.14 x 140 /60
Angular velocity = 14.653 rad / s
Speed = r x angular velocity
v = 15.55 x10-2 x 14.653 = 2.28 m/s = 2.3 m/s

2) Velocity of the centre of mass of the tire v is 18 m/s , r =32.5
The angular frequency = v / r
w = 18 / 32.5
w = 0.554 rad /s
w = 0.554 x 60 / 2 x 3.14 = 5.29 rpm

3) The velocity at the top edge of the tire is two times the velocity at the centre of mass
vt = 2 x v = 2 x 18
vt = 36.0 m/s

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