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

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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

Physics

1 answer:

inna [3.1K] · Answer 1 · 2026-04-01T21:38:59+03:00

To address the issue, it is essential to utilize the equations of Torque along with their definitions.

Torque is described as,

$\tau = I \alpha$

where,

I=Moment of Inertia

$\alpha =$ Angular acceleration

Additionally, Torque in relation to linear motion is indicated as,

$\tau = F*d$

with,

F = Force

d= distance

The provided parameters are as follows:

R = 30 cm = 0.3m

m = 1.5 kg

F = 20 N

r = 4.0 cm = 0.04 m

t = 4.0s

Thus, aligning the two equations, we find that:

$d*F = I\alpha$

For a wheel, the moment of inertia is expressed as,

I= mR², substituting yields

$d*F= \frac{mR^2a}{R}$

$d*F= mRa$

$a = \frac{rF}{ mR}$

$a = \frac{0.04*20}{1.5*0.3}$

$a=1.77 m/s^2$

Therefore, the wheel's velocity is

$V = a *t \\V=1.77*4 \\V=7.11 m/s$

Consequently, the right answer is D.