The solid right-circular cylinder of mass 500 kg is set into torque-free motion with its symmetry axis initially aligned with the fixed spatial line a–a. due to an injection error, the vehicle’s angular velocity vector ω is misaligned 5◦ (the wobble angle) from the symmetry axis. calculate to three significant figures the maximum angle φ between fixed line a–a and the axis of the cylinder.

30.95°

Explanation:

We need to define the moment of inertia of cylinder but in terms of mass, that equation say,

Replacing the values we have,

At the same time we can calculate the mass moment of intertia of cylinder but in an axial way, that is,

Finally we need to find the required angle between the fixed line a-a (I attached an image )

Replacing the values that we have,

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂