Question

A 12.0 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.

Answer 1

 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