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Question

Wheel A of radius rA=10 cm is coupled by belt B to a wheel C of radius rc=25 cm. The angular speed of the wheel A is increased from rest at a constant rate of 1.6 rad/s2. Find the time needed for wheel C to reach an angular speed of 100 rev/min, assuming that the belt does not slip.


A
4 seconds
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B
9 seconds
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C
16 seconds
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D
25 seconds
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Solution

The correct option is C 16 seconds
Given that
Radius of wheel A, rA=10 cm
Radius of wheel C, rC=25 cm
Initial angular speed ω0=0
Angular acceleration of the wheel A =1.6 rad/s2
Let angular acceleration of wheel A be αA and angular acceleration of wheel C be αC.
Since they are connected by the same belt,
Tangential acceleration of wheel A = tangential acceleration of wheel B
αArA=αCrC
αC=αA(rArC)=1.6×(1025)
αC=0.64 rad/s2
Now, ωC=αCt
t=ωCαC
t=100 rev/min0.64 rad/sec2
t=100×2π60 rad/sec0.64 rad/sec2
t16 sec

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