An object of mass M = 12.5 kg is attached to a cord that is wrapped around a whe

Question

An object of mass M = 12.5 kg is attached to a cord that is wrapped around a wheel of radius r = 11.5 cm (see figure). The acceleration of the object down the frictionless incline is measured to be a = 2.00 m/s2and the incline makes an angle ? = 37.0

An object of mass M = 12.5 kg is attached to a cord that is wrapped around a wheel of radius r = 11.5 cm (see figure). The acceleration of the object down the frictionless incline is measured to be a = 2.00 m/s2 and the incline makes an angle ? = 37.0 degree with the horizontal. Assume the axle of the wheel to be frictionless. Determine the tension in the rope. Determine the moment of inertia of the wheel. Determine the angular speed of the wheel 2.60 s after it begins rotating, starting from rest.

Explanation / Answer

mgsin37 - T = ma

12.5 x 9.8sin37 - T = 12.5 x 2

T = 48.72 N

b) T.r = I x alpha = I x a/r

I = 48.72 x 0.115^2 / 2   =0.322 Kg.m^2

c) alpha = a/r = 2 / 0.115 =17.39 rad/s2

w = alpha x t = 17.39 x 2.60 =45.22 rad/s

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