Question

A bicycle wheel has a mass of 2.0 kg and a radius of 60 cm. With the wheel initially at rest, a torque of 0.36 N-m is then applied. What is the angular speed of the tire after 5 seconds? The moment of inertia of a wheel is mR².

A. 0.5 rad/s

B. 1.0 rad/s

C. 1.5 rad/s

D. 2.5 rad/s

E. 5.0 rad/s

Answer 1

Sol::

Given data

Mass(m)= 2.0 kg
Radius(R)= 60 cm
= 0.6 m
Torque(T)= 0.36 N-m
Time(t)=5 s

Using Newton's second law for rotationional form
As
ΣT= I? ................................................(1)

Where I is the moment of inertia of wheel
i. e I =mR²
= 2*(0.6)²
= 0.72 kg.m²

And  
Angular acceleration ? = w/t
? =w/5
So from equation(1) we have

ΣT= I?
0.36= 0.72*w/5
w= 2.5 rad/s

So option (D) is correct
  

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