A rope is wrapped around a wheel of diameter, 50cm. The wheel ismounted with fri

Question

A rope is wrapped around a wheel of diameter, 50cm. The wheel ismounted with frictionless bearings on an axle through its center. Ablock of 15kg is suspended from the end of the rope. When thesystem is released from rest the block falls 5.0m in 2.0s.

a) what is the linear acceleration of the falling block?
I got =2.5 rad/sec2 by using the=0+t formula

b) what is the angular acceleration of thewheel, assuming the rope does not slip on the wheel?
This part I need help to figure out I cannotfigure out what formula I need to get this answer

c)What is the tension in the rope?
For this I summed the forces which weremg-T=ma and got T=109.5N

What is the moment of inertia of the wheel? Note: This should becalculated from data in the problem and not from the formula for Iof a disk or a hoop.
I am lost with how to do this without usingthe I formula the teacher says not to use

Explanation / Answer

(a) You got the right answer for the wrong reasons. Youare supposed to use linear kinematics (this is why they tell youthe distance fallen and the time)... .     acc = 2 * distance fallen /time2 = 2 * 5.0 /2.02   =    2.50m/s2 . (b) = a / r =   2.50 m/s2 / 0.50 m    =      5.00rad/s2 . (c) You're a-ok here...   forces acting on theblock:      mg - T = ma    solve forT,    109.5 N . (d) This is a little sneaky. The tension provides torqueto the wheel, and you have to use .       torque = I        (this is Newtons secondlaw for rotation... like    Force = ma) .        T * r   = I .    I = T r /    = 109.5 * 0.5 / 5.00 =     10.95 kg-m2            (you cant use the formulas because they only apply to uniformobjects, and you are not told if this is a uniform disk orwheel) . (c) You're a-ok here...   forces acting on theblock:      mg - T = ma    solve forT,    109.5 N . (d) This is a little sneaky. The tension provides torqueto the wheel, and you have to use .       torque = I        (this is Newtons secondlaw for rotation... like    Force = ma) .        T * r   = I .    I = T r /    = 109.5 * 0.5 / 5.00 =     10.95 kg-m2            (you cant use the formulas because they only apply to uniformobjects, and you are not told if this is a uniform disk orwheel)

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