Important: Regard m , g , T , r and I as positive quantities. The accelerations
ID: 1980739 • Letter: I
Question
Important: Regard m, g, T, r and I as positive quantities. The accelerations a and may be positive or negative, depending on direction. In the coordinate system assumed "positive" means up for linear quantities and counterclockwise for angular quantities.
Write both sides of Newton's 2nd law for the falling weight: the net force, given in terms of the tension T and the gravity force mg should equal the weight's mass times it acceleration.
Write both sides of Newton's 2nd law in rotational form for the wheel. Express the torque in terms of the tension T and wheel radius r. Express the angular acceleration in terms of –a/r, since a counterclockwise angular acceleration is positive, but this corresponds to a negative (downward) linear acceleration of the hanger. A counterclockwise torque is positive.
Finally, substitute a = –r into your formula and solve it for I to obtain the required formula in terms of the variables m, g, r and .
A hanger of mass m is attached to a light string that is wrapped around the rim of a wheel of radius r. The wheel is released, allowing the weight to fall and cause the wheel to accelerate rotationally. In the experiment, the rotational acceleration is measured. The acceleration of gravity is g (defined as a positive quantity), and the moment of inertia is I. Work out a formula for I by following the stteps given below.All answers are formulas, and should contain only symbols from the following set: hanger mass m (type "m"), acceleration of gravity g (type "g"), moment of inertia I (type "I"), radius r (type "r"), linear acceleration of the falling weight a (type "a"), string tension T (type "T"), and rotational acceleration (type "alpha"). Use the previewer ("eye" icon) to check the formatting of your answer before you submit it. Check this link for help on entering formulas:
Explanation / Answer
1. T - mg = ma 2. Tr = -Ia/r 3. a = -mg/((I/r^2) + m) 4. I = (((mg)/(ralpha)) - m)r^2