Physics, 09.04.2020 20:56 3kp

A 5 kg uniform disk with a 40 cm radius swings without friction about a nail through a point 10 cm from the rim. It is released from rest from a position with its center above the nail.(a) What is its angular velocity when the center is directly below the nail?(b) What is its angular acceleration when the center is level with the nail?(c) Suppose it hangs with its center directly below the nail. If it is pushed a small distance from this equilibrium position then what is its period of small oscillations?

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Answer from: MIC620

(a) Angular velocity is 8.31 rad/s

(b) Angular acceleration is 17.29 rad/s²

Explanation

Given:

Mass, m = 5 kg

Radius, r = 40 cm

Distance, x = 10 cm

(a)

Angular velocity, ω = ?

In this case, energy is conserved.

$\frac{1}{2} I w^2 = mg (2a)\\\\w^2 = \frac{4mag}{I} \\\\w = \sqrt{\frac{4mag}{I} }$

where,

I = moment of Inertia

g = gravity

a = distance between the nail and the center

To find I of nail:

I_n_a_i_l = I_c_e_n_t_e_r + ma^2

and

$I_c_e_n_t_e_r = \frac{mr^2}{2} \\\\I_c_e_n_t_e_r = \frac{5 X 0.4^2}{2} \\\\I_c_e_n_t_e_r = 0.4 kg.m^2$

On substituting the value:

$I_n_a_i_l = 0.4 + 5 ( 0.4 - 0.1) ^2\\\\I_n_a_i_l = 0.4 + 0.45\\\\I_n_a_i_l = 0.85 kg.m^2$

So, ω is:

$w = \sqrt{\frac{4 X 5X 9.8 X 0.3}{0.85} } \\\\w = 8.31 rad/s$

(b)

Angular acceleration, α = ?

We know:

$\alpha = \frac{t}{I}$

where,

ζ = torque

I = moment of Inertia

To calculate torque:

$t = F X a\\ \\ = mg X a\\\\= 5 X 9.8 X 0.3\\\\= 14.7 Nm$

Substituting the value we get:

$\alpha = \frac{14.7}{0.85} \\\\\alpha = 17.29 rad/s^2$

Thus, the angular acceleration is 17.29 rad/s²

(c)

Period of oscillation, T = ?

We know:

$T = 2\pi \sqrt{\frac{I}{mga} }$

On substituting the value:

$T = 2 X 3.14 X\sqrt{\frac{0.85}{5 X 9.8X0.3} } \\\\T = 1.51 s$

Answer from: Quest

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account. she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem. she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem. her desire for the new hairstyle is in conflict with her honesty and integrity.

d. if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it. the amount she has in her account is not the problem. and if i may suggest, she might as well close her checking account, and put the money where it'll work for her. it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now. under no circumstances should he ask for a higher limit.

b. he can ask for the grace period to be extended. but that's no solution, the bank will almost certainly refuse anyway, and there are much better options. he knew the rules of his credit card when he started using it.

c. he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d. he definitely should pay the minimum otherwise they could shut down his card. he should also pay as much more as he possibly can. he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices. what he has to do: pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

Answer from: Quest

The answer is a i think

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