A thin, straight metal bar with a length of 0.450 m is attached to an axle at on

Question

A thin, straight metal bar with a length of 0.450 m is attached to an axle at one end so that it can rotate at a constant speed in a circle on a horizontal. frictionless table. The rotation axis is perpendicular to the length of the metal bar. The metal bar is initially spinning at 0.43 rad/s. Its moment of inertia around the axis is 2.80 times 10^-3 kg.m^2. While the bar is rotating, a mechanical engineer gently drops a small, very strong magnet onto the bar at a distance of 0.300 m from the axle, and the magnet attaches itself firmly there. The magnet can be treated as a point mass. If the new rotation speed is now 0.200 rad/sec, find the mass of the metal bar and the mass of the magnet.

Explanation / Answer

A thin straight metal bar with a length of 0.450 m is attached to an axle at one end so that it can rotate at a constant speed in a circle on a horizontal frictionless table.

answer: Length =0.450 m

rotation axis is perpendicular to the length of the metal bar

rotation speed w=0.43 rad/s

the M.I of the metal bar is I =0.00280 kg.m-2

Find the mass of the metal bar and magnet

Since I=1/3 ML2  for metal bar so M=3*I/L2 or M=3*0.00280 /0.450^2= 0.0415 kg or 41.5 g

Angular momentum =Iw=0.00280*0.43= 0.0012

a smaller mass acquire the angular momentum of rotating metal bar

thus Inew*Wnew=0.0012

=>Inew*0.2=0.0012

=>Inew=0.0060

But this Moment of inertia is due to metal bar and point magnet

so Inew=0.00280+mr2=0.00280+m*0.3^2

=>0.0060 - 0.00280=m*0.09

=>m=0.0032/0.09= 0.0356 kg or 35.6 gm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.