Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. neglect the mass of the axle and sprocket. if a force of 20 n is applied tangentially to a sprocket of radius 4 cm for 4 seconds, what linear speed does the wheel achieve, assuming it rolls without slipping?

a) 3 m/s
b) 24 m/s
c) 5.9 m/s
d) 7.1 m/s

To solve the problem it is necessary to apply the Torque equations and their respective definitions.

The Torque is defined as,

Where,

I=Inertial Moment

Angular acceleration

Also Torque with linear equation is defined as,

Where,

F = Force

d= distance

Our dates are given as,

R = 30 cm = 0.3m

m = 1.5 kg

F = 20 N

r = 4.0 cm = 0.04 m

t = 4.0s

Therefore matching two equation we have that,

For a wheel the moment inertia is defined as,

I= mR2, replacing we have

Then the velocity of the wheel is

Therefore the correct answer is D.

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