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 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 disk, because it has a smaller moment of inertia and thus accelerates faster.

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 spins with arms extended and then pulls them in. Which principle explains why her angular velocity increases?

Accepted Answer

Conservation of angular momentum

Question 4

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

Accepted Answer

Net force and net torque are both 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 equation gives the rotational kinetic energy of a rotating object?

Accepted Answer

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

Question 8

A hydraulic lift uses Pascal’s Principle. If the input piston has area $$A_1$$ and the output piston has area $$A_2$$, what is the output force $$F_2 if $$the input force is $$F_1$$?

Accepted Answer

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

Question 9

A submarine is at depth $$d in $$seawater with density $$\rho. $$What is the absolute pressure at this depth?

Accepted Answer

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

Question 10

A block of wood floats in water. Which statement is true about the buoyant force?

Accepted Answer

The buoyant force equals the weight of the displaced water.

Question 11

A fluid flows through a pipe with varying diameter. Which equation expresses the conservation of mass (equation of continuity)?

Accepted Answer

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

Question 12

A diver releases air bubbles underwater. As the bubbles rise, what happens to their volume and why?

Accepted Answer

Volume increases because pressure decreases.

Question 13

Which property is measured by Young’s modulus?

Accepted Answer

Resistance to deformation under tensile stress

Question 14

A spinning wheel has angular momentum $$L. If no $$external torque acts, what happens to $$L$$?

Accepted Answer

$$L$$ remains constant

Question 15

A fluid flows faster through a narrow section of a pipe than a wide section. Which principle explains this?

Accepted Answer

Equation of continuity

Question 16

A ball is submerged in water and its apparent weight is measured. How can the buoyant force be determined?

Accepted Answer

Buoyant force equals the difference between actual weight and apparent weight.

Question 17

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

Accepted Answer

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

Question 18

A rod is pivoted at one end and held horizontally. Where is its center of gravity?

Accepted Answer

At the midpoint of the rod

Question 19

Which of the following best describes laminar flow?

Accepted Answer

Fluid moves in smooth, parallel layers

Rotational Motion, Equilibrium, and Fluid Mechanics: Study Notes

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