Rotational Motion - I have the answer but I don't know how to get there

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SUMMARY

The discussion centers on calculating angular acceleration, angular speed, and the number of turns for a bike wheel subjected to a torque of 1 N.m. Given the wheel's radius of 35 cm and mass of 0.75 kg, the angular acceleration is determined to be 10.9 rad/s². After 5 seconds from rest, the angular speed reaches 54.4 rad/s, resulting in a total of 21.7 turns during that period. The relationship between torque, moment of inertia, and angular acceleration is established through the equation τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.

PREREQUISITES
  • Understanding of torque and its units (N.m)
  • Familiarity with moment of inertia (I = MR²)
  • Basic knowledge of angular motion equations
  • Ability to perform calculations involving radians and angular speed
NEXT STEPS
  • Study the relationship between torque and angular acceleration in rotational dynamics
  • Learn how to calculate moment of inertia for different shapes
  • Explore angular motion equations, including θ = ω₀t + 0.5αt²
  • Practice problems involving rotational motion and energy
USEFUL FOR

Students preparing for physics exams, particularly those focusing on rotational dynamics, as well as educators seeking to clarify concepts of torque and angular motion.

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A torque of 1 N.m is applied to a bike wheel of radius 35 cm and mass 0.75 kg. Treating the wheel as a hoop (I=MR^2)

A. What is it's angular acceleration? Answer - 10.9 rad/s^2
B. If the wheel starts from rest, what is its angular speed after 5 seconds? Answer - 54.4 rad/s
C. How many turns does it do in those 5 seconds? Answer 21.7 turns

I'm trying to study for my exam, and I'm stuck on this problem for our practice test. My professor gave us answers, but I'm just at a loss as to how to get the answers. Can anyone explain how to solve this problem? Thanks!
 
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