The angular velocity of the wheel depends on the mass, radius and the
mode of rotation of the wheel (with or without slipping).
- The angle velocity at the bottom of the incline, ω ≈ <u>4.43 rad/sec</u>
Reasons:
The given parameters are;
Radius of the wheel, r = 2.0 m
Height of the incline, h = 8.0 m
Required:
Angular velocity of the wheel at the bottom of the incline.
Solution:
The potential energy of the wheel at the top of the hill, P.E. = m·g·h

Where;
v = The translational velocity of the wheel = ω·r
I = The moment of inertia of the wheel = m·r²
Therefore'

At the bottom of the hill, the potential energy is converted to kinetic energy
Therefore;
P.E. = Sum of K.E.
m·g·h = m·r²·ω²
g·h = r²·ω²

Where;
g = Acceleration due to gravity ≈ 9.81 m/s²
Therefore;

- The angular velocity of the of the wheel at the bottom of the incline, ω ≈ 4.43 rad/sec
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