Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted wi

Question

Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted with its axle fixed in a horizontal position. A 50-g mass is hung from a string wrapped around the periphery of the tire. The wheel is held stationary with the weight hanging as shown and then released. The wheel starts to spin and spins faster and faster until the string slips off 5 seconds after release. An electronic device counts the number of spokes that pass in front of it and sends the information to a computer. This allows us to obtain a 50 g measurement of the angular speed of the wheel. The readings of the display device are summarized in the graph below. 10-- 60 8.0 4 0 Time (s) 20

Explanation / Answer

given data

mass m=5g=0.05kg

initial nagular velocity of the wheel, w1 = 0

2)

the angular velocityof the wheel, w2 = (10/16)*2*pi rad/s

= 3.925 rad/s

3)

angular acceration of the wheel = (w2-w1)/t

= (3.925-0)/5

= 0.785 rad/s^2

4)

accelaration of the ahanging mass, a_tan = r*alpha

= 0.3*785

= 0.236 m/s^2

5) Initail tension, T = m*g

= 0.05*9.8

= 0.49 N

final tension, T = m*g - m*a

= 0.05*9.8 - 0.05*0.236

= 0.4782 N

6) Torque = T*r*sin(90)

= 0.4782*0.3*1

= 0.143 N.m

7) Torque = I*alpha

I = Torque/alpha

= 0.143/0.785

I= 0.183 kg.m^2

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