A12.0 kg object is attached to a cord that is wrapped around a wheel of radius 10.0 cm. the acceleration of the object down the frictionless incline is measured to be 2.00 m/s2. assuming the axis of the wheel to be frictionless, determine a. the tension in the rope, b. the moment of inertia of the wheel, and c. the angular speed of the wheel 2.00 s after it begins rotating, starting from rest.

 a) We use the formula:

T = [g sinθ – a] * m

where g is gravity, θ is the angle, a is acceleration, m is mass

T = [9.81 sin37 - 2.00] * 12 = 46.85 N 

b) We use the formula for moment of interia:

I = T * r² / a

I = 46.85 * 0.10² / 2.00 = .2343 kg∙m² 

c) The formula we can use here is:

w = α * t = (a/r) * t

w = (2/.10) * 2

w = 40 rad/sec

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