An old penny-farthing bicycle has a front wheel with diameter D = 120.0 cm and a

Question

An old penny-farthing bicycle has a front wheel with diameter D = 120.0 cm and a back wheel with diameter d = 40.0 cm. A cyclist rides this bicycle to the right with a velocity v = 10 km/hour. a) What is the direction of the angular velocity vector of the front wheel of the bicycle? Describe, or make a drawing that indicates the direction. b) How many revolutions per minute does the front wheel make? c) What is the velocity of the top of the back wheel? A leaf is stuck on a spoke of the front wheel at 40.0 cm from the axis. d) What is the velocity of the leaf when it is at its lowest point? e) The cyclist is steadily accelerating to a new velocity of 20.0 km/hour in 15 seconds. Calculate the torque acting on the back wheel during the acceleration.

Explanation / Answer

given

v = 10 km/hr = 10*5/18 = 2.78 m/s

D = 120 cm

d = 40 cm

a) in to the page.

because, v = w cross r

b) radius, r = d/2 = 40/2 = 20 cm = 0.2 m

w = v/r

= 2.78/0.2

= 13.9 rad/s

= 13.9*60/(2*pi)

= 132.7 rev/min

c) v_top = 2*v

= 2*2.78

= 5.56 m/s

d) v_lowest = 0

e) angular acceleration of back wheel, alfa = (w2 - w1)/t

= ( (v2 - v1)/r)/t

= ( (2*2.78 - 2.78)/0.2)/15

= 0.927 rad/s^2

Torque, T = I*alfa

so, need I(moment of inertia of wheeel) to fond Torque)

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