Q: Which equation represents Bernoulli's equation for fluid flow?

$$P + \frac{1}{2}\rho v^2$ + \rho g y = \text{constant}$$

Q: A steel rod of length $$L_0 = 2.00$$\ \mathrm{m}$$ at 20$$\degree C$$ is heated to 40$$\degree C$$. If the coefficient of linear expansion is $$\alpha = 12 \times $$10^{-6}$$\ \mathrm{C}^{-1}$$, what is the change in length?

$$\Delta L = 4.8 \times 10$$^{-4}$$\ \mathrm{m}$$

Question 1

A solid disk of mass $$m$$ and radius $$R$$ rotates about its central axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2}mR^2$

Question 2

A force $$\vec{F} is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$	heta$$ with $$r. $$What is the magnitude of the torque produced?

Accepted Answer

$$	au = rF\sin	heta$$

Question 3

Which equation correctly relates angular acceleration $$\alpha to $$torque $$	au$$ and moment of inertia $$I$$?

Accepted Answer

$$\alpha = 	au/I$$

Question 4

A wheel starts from rest and accelerates at $$2\ \mathrm{$$rad/s^2$$}$$ for $$5$$ seconds. What is its angular velocity at $$t=5 s$$?

Accepted Answer

$$\omega = 10\ \mathrm{rad/s}$$

Question 5

Which of the following is the correct expression for rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2}I\$$omega^2$$

Question 6

A uniform rod of length $$L$$ and mass $$m$$ rotates about an axis through one end perpendicular to its length. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3}mL^2$

Question 7

A block of mass $$m is $$submerged in a fluid of density $$\rho_f. $$What is the buoyant force acting on the block?

Accepted Answer

$$F_b = \rho_f V g$$

Question 8

Which principle states that the pressure applied to a confined fluid is transmitted undiminished throughout the fluid?

Accepted Answer

Pascal's Principle

Question 9

A fluid flows through a pipe with cross-sectional areas $$A_1$$ and $$A_2$$ and velocities $$v_1$$ and $$v_2. $$Which equation expresses the continuity equation for incompressible flow?

Accepted Answer

$$A_1v_1 = A_2v_2$$

Question 10

Which equation represents Bernoulli's equation for fluid flow?

Accepted Answer

$$P + \frac{1}{2}ho v^2$ + ho g y = 	ext{constant}$$

Question 11

A gas at pressure $$P$$, volume $$V$$, and temperature $$T$$ obeys the ideal gas law. Which equation is correct?

Accepted Answer

$$PV = nRT$$

Question 12

What is the relationship between Celsius and Kelvin temperature scales?

Accepted Answer

$$T(K) = T(\degree C) + 273.15$$

Question 13

A steel rod of length $$L_0 = 2.00$$\ \mathrm{m}$$ at 20$$\degree C$$ is heated to 40$$\degree C$$. If the coefficient of linear expansion is $$\alpha = 12 	imes $$10^{-6}$$\ \mathrm{C}^{-1}$$, what is the change in length?

Accepted Answer

$$\Delta L = 4.8 	imes 10$$^{-4}$$\ \mathrm{m}$$

Question 14

Which law states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other?

Accepted Answer

Zeroth Law of Thermodynamics

Question 15

A $$0.5\ \mathrm{kg}$$ block of ice at $$-10\degree C is $$heated until it becomes water at $$20\degree C. $$Given $$c_{ice} = 0.5\ \mathrm{Cal/g\cdot C}$$, $$L_f = 79.7\ \mathrm{Cal/kg}$$, and $$c_{water} = 1\ \mathrm{Cal/g\cdot C}$$, which equation gives the total heat required?

Accepted Answer

$$Q = m c_{ice} \Delta T + m L_f + m c_{water} \Delta T$$

Question 16

Which equation expresses the first law of thermodynamics?

Accepted Answer

$$\Delta E_{int} = Q - W$$

Question 17

A cylinder contains an ideal gas at $$P = 1.0 	imes 10^5$\ \mathrm{Pa}$$, $$V = 0.024\ \mathrm{m^3$}$$, and $$T = 273\ \mathrm{K}. $$How many moles of gas are present? ($$R = 8.31\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$n = 1.06$$

Question 18

A ball is dropped from rest and falls under gravity. Which equation gives its velocity after time $$t$$?

Accepted Answer

$$v = v_0$ + at$$

Question 19

Which of the following is NOT an assumption of the ideal gas model?

Accepted Answer

Gas particles have attractive forces

Rotational Dynamics, Fluid Dynamics, and Thermodynamics: Structured Study Notes

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