NOTE : These numbers are not realistic. Suppose that, in procedure 1, you measur

Question

NOTE: These numbers are not realistic.

Suppose that, in procedure 1, you measured the moment of inertia of the system as I = 6.12 kg-m2.

a) In trial 1:the system is initially spinning at angular speed o = 2.68 rad/s. After you drop the free disk of mass 716 g on it, the system rotates at f = 2.43 rad/s. Find:
- the moment of inertia of the free disk: Idisk = ___ kg-m2
- the radius of the free disk: rdisk = ____ m

b) In trial 3: suppose the system is initially spinning at angular speed o = 4.52 rad/s. After you drop a cube of mass 563 g on it, the system rotates at f = 4.24 rad/s. Find:
- the moment of inertia of the cube: Icube = ____ kg-m2
- the length of one side of the cube: Lcube = ____ cm

Explanation / Answer

Given Io=I1=6.12kg·m²,

do=2.68rad/s,

o=2.68rad/s,

f=2.43rad/s,

m2=0.716kg

A )From conservation of angular momentum, we know:
Io·o = If·f

Solve for If, which also equals I1+I2

If = Io(o/f) = I1+I2

I2 = Io((o/f)-1) = 0.62 kg·m²

The moment of inertia of a disc is given by:

I = ½mr²

Then solve for radius:

r = (2I/m)

r2 = (2·I2/m2) = 1.6m

= (2·0.62/0.716) = 1.35m

B)

Io=I1=6.12kg·m²,

o=4.52rad/s,

f=4.24rad/s,

m2=0.563kg

From conservation of angular momentum, we have:

Io·o = If·f = (Io+I2)f

Solving for cube's moment of inertia gives:

I2 = Io((o/f)-1) = 5.52 kg·m²

Moment of inertia of block (cube) is:

I2 = (m/12)(a²+b²) = (0.563/6)a²

a = (6I2/m) = 7.66

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

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