Q: Which equation correctly relates angular displacement $$\theta$$, angular velocity $$\omega$$, and angular acceleration $$\alpha$$ for rotational motion starting from rest?

$$\theta = \frac{1}{2} \alpha t^2$

Question 1

A solid disk and a hollow ring, both with mass $$m$$ and radius $$R$$, are released from rest at the top of an incline. Which will reach the bottom first, and why?

Accepted Answer

The solid disk, because it has a smaller moment of inertia.

Question 2

Which equation correctly relates angular displacement $$	heta$$, angular velocity $$\omega$$, and angular acceleration $$\alpha$$ for rotational motion starting from rest?

Accepted Answer

$$	heta = \frac{1}{2} \alpha t^2$

Question 3

A figure skater increases her spin rate by pulling her arms in. Which principle explains this phenomenon?

Accepted Answer

Conservation of angular momentum

Question 4

If a torque $$	au is $$applied to a wheel of moment of inertia $$I$$, what is the angular acceleration $$\alpha$$?

Accepted Answer

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

Question 5

A beam is supported at its ends and a weight is placed at its center. What must be true for the beam to be in static equilibrium?

Accepted Answer

Net force and net torque must both be zero.

Question 6

A steel wire is stretched by a force $$F. If $$its original length is $$L$$ and its cross-sectional area is $$A$$, what is the tensile stress?

Accepted Answer

$$\frac{F}{A}$$

Question 7

Which of the following best describes the elastic limit of a material?

Accepted Answer

The maximum strain a material can withstand and still return to its original shape.

Question 8

A diver is submerged at a depth $$d in $$water. What is the absolute pressure at this depth?

Accepted Answer

$$P = P_0$ + \rho g d$$

Question 9

A hydraulic lift uses Pascal’s Principle. If a force $$F_1 is $$applied to a small piston of area $$A_1$$, what is the force $$F_2$$ exerted by a larger piston of area $$A_2$$?

Accepted Answer

$$F_2$$ = $$F_1$$ \frac{$$A_2$$}{$$A_1$$}$$

Question 10

An object floats in water with half its volume submerged. What can be said about its density $$\rho_{object}$$ compared to water $$\rho_{water}$$?

Accepted Answer

$$\rho_{object} = \frac{1}{2} \rho_{water}$$

Question 11

Which equation expresses the conservation of angular momentum for a system with zero external torque?

Accepted Answer

$$L_{initial} = L_{final}$$

Question 12

A fluid flows through a pipe with varying diameter. Which equation describes the relationship between the areas and velocities at two points?

Accepted Answer

$$A_1$$ $$v_1$$ = $$A_2$$ $$v_2$$

Question 13

A block of wood is placed in water and its apparent weight is measured. How can the buoyant force be determined?

Accepted Answer

By subtracting the apparent weight from the actual weight.

Question 14

Which equation gives the speed of fluid exiting a hole at depth $$h$$ below the surface, according to Torricelli’s equation?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 15

A rotating object has angular velocity $$\omega$$ and moment of inertia $$I. $$What is its rotational kinetic energy?

Accepted Answer

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

Question 16

Which of the following is NOT a state of matter?

Accepted Answer

Plasma

Question 17

A fluid is flowing in a pipe and the flow is smooth and orderly. What is this type of flow called?

Accepted Answer

Laminar flow

Question 18

If a force is applied at a distance $$r$$ from a pivot, what is the torque produced?

Accepted Answer

$$	au = r 	imes F$$

Question 19

A column of mercury in a barometer is 760 mm high. What does this height represent?

Accepted Answer

Absolute pressure at sea level

Rotational Motion, Equilibrium, and Fluid Mechanics: Study Notes

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