A bicycle wheel is mounted on a fixed, frictionless axle. A light string is woun

Question

A bicycle wheel is mounted on a fixed, frictionless axle. A light string is wound around the wheel's rim, and a weight is attached to the string at its free end. The diagrams below depict the situation at three different instants: At t = t_1, the weight is released from rest. At t = t_2, the weight is falling and the string is still partially wound around the wheel. At t = t_3, the weight and string have both reached the ground. What is the direction of the angular velocity omega^rightarrow of the wheel at each time shown? If | omega^rightarrow = 0 at any time, state so explicitly. Explain. What is the direction of the wheel's angular acceleration alpha^rightarrow at each time shown? If | alpha^rightarrow | = 0 at any time, state so explicitly. Explain. Rank the magnitudes of the centripetal acceleration of point A at the three times shown (a_A1, a_A2, a_A3). If any of these is zero, state so explicitly. Explain your reasoning.

Explanation / Answer

a) Direction of angular velocity can be given using right hand rule

If we curl our right hand fingers along the direction of wheel motion then our thumb will point the direction of angular velocity

initially wheel was at rest so there is no direction of angular velocity at time t=0

after that wheel start turning clockwise so direction of angular velocity will be into the page at time t=t1

direction will remain same at time t=t2 also

b) As here angular velocity is increasing so direction of angular acceleration will also be in same direction

at t=0 direction of angular acceleration is into the page

same at time t=t1

at time t=t2 no torque is applying so wheel will rotate with constant angular velocity hence angular acceleration become zero

c) Same torque is acting at time t=0 and t=t1 due to the weight of mass m

so angular acceleration will be smae at t=0 and t=t1 and it is zero at t=t2 as mass is not attached with wheel now

aA1= aA2 > aA3

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