Question

b) Assume the rod is 0.60 m long and has a mass of 0.50 kg, and the clay blob has a mass of 0.20 kg and moves at an initial velocity of 8.0 m/s. Calculate the final angular velocity of the rod. Be sure to put units in your calculation and show the resulting units in your answer.

Answer 1

The final angular velocity of the rod is 2.40 rad/s.

Step-by-step explanation:

We can use the principle of conservation of angular momentum to answer this question. The initial angular momentum of the system is equal to the final angular momentum. Initially, the clay blob is at rest, so its angular momentum is zero. The rod has an initial angular velocity of 10.0 rad/s, and since there are no external torques acting on the system, its initial angular momentum is given by:

Li = Irod * ωi

where Li is the initial angular momentum, Irod is the moment of inertia of the rod, and ωi is the initial angular velocity of the rod.

The final angular momentum is given by:

Lf = Irod * ωf + Iblob * ωblob

where Lf is the final angular momentum, Iblob is the moment of inertia of the clay blob, and ωf and ωblob are the final angular velocities of the rod and the clay blob, respectively.

Since the clay blob is mounted on the rod, its final angular velocity will be the same as the rod's, so we can rewrite the equation as:

Lf = (Irod + Iblob) * ωf

To find the final angular velocity, we can rearrange the equation:

ωf = Lf / (Irod + Iblob)

Plugging in the given values, we have:

ωf = (0.5 kg)(0.60 m)(8.0 m/s) / [(1/3)(0.50 kg)(0.60 m)2 + 0.20 kg(0.10 m)2]

ωf = 2.40 rad/s

Answer 2

The correct answer is "6.96 rad/s".

Step-by-step explanation:

The given values are:

Length,

L = 0.6 m

Mass,

m₁ = 0.5 kg

m₂ = 0.2 kg

Initial velocity,

V = 8 m/s

Now,

The final angular velocity will be:

⇒
`\omega =(6m_1V)/((4m_1+3m_2)L)`

By substituting the values, we get

⇒
`=(6* 0.2* 8)/((4* 0.2+3* 0.5)0.6)`

⇒
`=(9.6)/(1.38)`

⇒
`=6.96 \ rad/s`