Q: A large ceiling fan has five blades, each with a mass of 2.0 kg and a length of 0.75 m. If the fan spins at 1.2 revolutions per second, what is the angular velocity $$\omega$$?

$$\omega = 2\pi \times 1.2 = 7.54\ \mathrm{rad/s}$$

Q: A cooler with a volume of 0.050 m$$^3 is $$filled with water. What is the mass of water inside, assuming the density of water is $$1000\ \mathrm{kg/m^3$}$$?

$$m = \rho V = 1000 \times 0.050 = 50\ \mathrm{kg}$$

Q: A block is floating in water with 75% of its volume submerged. What is the ratio of the block's density to the water's density?

$$\frac{\rho_{\text{block}}}{\rho_{\text{water}}} = 0.75$$

Question 1

A block of wood has a mass of 2.5 kg and a volume of 0.003 m$$^3. $$What is its density?

Accepted Answer

$$\frac{2.5}{0.003} = 833\ \mathrm{kg/m^3$}$$

Question 2

Which principle explains why a boat floats on water?

Accepted Answer

Archimedes' Principle

Question 3

A large ceiling fan has five blades, each with a mass of 2.0 kg and a length of 0.75 m. If the fan spins at 1.2 revolutions per second, what is the angular velocity $$\omega$$?

Accepted Answer

$$\omega = 2\pi 	imes 1.2 = 7.54\ \mathrm{rad/s}$$

Question 4

During the 'spin up' period of a ceiling fan, which of the following quantities increases?

Accepted Answer

Angular velocity $$\omega$$

Question 5

A cooler with a volume of 0.050 m$$^3 is $$filled with water. What is the mass of water inside, assuming the density of water is $$1000\ \mathrm{kg/m^3$}$$?

Accepted Answer

$$m = ho V = 1000 	imes 0.050 = 50\ \mathrm{kg}$$

Question 6

A tightrope walker uses a long, heavy pole to help maintain balance. What is the primary physical reason this helps?

Accepted Answer

It increases the moment of inertia, making it harder to rotate and easier to balance.

Question 7

Suppose a balance pole has mass $$m$$ and length $$L. $$What is its moment of inertia about its center?

Accepted Answer

$$I = \frac{1}{12} m L^2$

Question 8

A block is floating in water with 75% of its volume submerged. What is the ratio of the block's density to the water's density?

Accepted Answer

$$\frac{ho_{	ext{block}}}{ho_{	ext{water}}} = 0.75$$

Question 9

Which of the following best describes the change in kinetic energy of a fan blade as it spins up from rest?

Accepted Answer

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

Question 10

A swimmer is floating in a lake. If the swimmer's mass is 70 kg and the volume displaced is 0.068 m$$^3$$, what is the density of the swimmer?

Accepted Answer

$$\rho = \frac{70}{0.068} = 1029\ \mathrm{kg/m^3$}$$

Question 11

A physical system consists of a long, uniform rod of length $$L$$ and mass $$M$$ pivoted at its center. Where is the center of mass located?

Accepted Answer

At the midpoint of the rod

Question 12

A block is completely submerged in water. Which force acts upward on the block?

Accepted Answer

Buoyant force

Question 13

If a fan blade rotates with angular velocity $$\omega$$ and has moment of inertia $$I$$, what is its rotational kinetic energy?

Accepted Answer

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

Question 14

A cooler is filled with water and floats in a lake. If the cooler is 80% submerged, what does this indicate about the cooler's average density compared to water?

Accepted Answer

The cooler's average density is 80% that of water.

Question 15

A tightrope walker holds a pole horizontally and rotates it about its center. If the pole has mass $$m$$ and length $$L$$, what is the magnitude of its angular momentum at angular velocity $$\omega$$?

Accepted Answer

$$L = I \omega = \frac{1}{12} m L^2$ \omega$$

Question 16

Which of the following is true about the buoyant force acting on a submerged object?

Accepted Answer

It equals the weight of the fluid displaced.

Question 17

A block of mass $$m is $$dropped into a cooler filled with water. What is the final equilibrium condition for the block?

Accepted Answer

The block floats if its density is less than water.

Question 18

A fan blade is spinning at angular velocity $$\omega. If $$the blade slows down to rest, what happens to its rotational kinetic energy?

Accepted Answer

It is converted to other forms, such as heat due to friction.

Question 19

A swimmer floats in water with 90% of their body submerged. What is their average density compared to water?

Accepted Answer

90% of the density of water

PHYS 151 Midterm Exam #4 Study Guide: Rotational Motion, Dynamics, and Fluid Mechanics

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