Question 1

A solid disk of mass $$2\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m} is $$spinning at $$120\ \mathrm{rpm}. $$What is its angular velocity $$\omega in$$ $$\mathrm{rad/s}$$?

Accepted Answer

$$\omega = 4\pi\ \mathrm{rad/s}$$

Question 2

A hose narrows from a cross-sectional area of $$0.01\ \mathrm{m}^2 to$$ $$0.005\ \mathrm{m}^2. If $$water enters the wide end at $$2\ \mathrm{m/s}$$, what is the speed at the narrow end? (Assume incompressible flow.)

Accepted Answer

$$4\ \mathrm{m/s}$$

Question 3

A car tire (modeled as a ring) of radius $$0.3\ \mathrm{m}$$ and mass $$10\ \mathrm{kg} is $$spinning at $$10\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$45\ \mathrm{J}$$

Question 4

A pendulum exhibits simple harmonic motion (SHM) with amplitude $$A$$ and angular frequency $$\omega. At $$what position is the speed of the pendulum bob maximum?

Accepted Answer

At the equilibrium position ($$x = 0)$$

Question 5

A sound source emits at $$500\ \mathrm{Hz}$$ and moves toward a stationary observer at $$30\ \mathrm{m/s}. If $$the speed of sound is $$340\ \mathrm{m/s}$$, what frequency does the observer hear?

Accepted Answer

$$f' = 547\ \mathrm{Hz}$$

Question 6

A $$0.5\ \mathrm{kg}$$ mass on a spring oscillates with $$k = 200\ \mathrm{N/m}. $$What is the angular frequency $$\omega of $$the oscillation?

Accepted Answer

$$\omega = 20\ \mathrm{rad/s}$$

Question 7

A firefighter uses a hose to spray water from ground level up to a window $$10\ \mathrm{m}$$ above. If the water exits the hose at $$20\ \mathrm{m/s}$$, what is the pressure difference required to achieve this height? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s}^2.)$$

Accepted Answer

$$\Delta P = 98,000\ \mathrm{Pa}$$

Question 8

A rotating solid sphere and a ring, both with mass $$M$$ and radius $$R$$, roll without slipping down the same incline from rest. Which reaches the bottom first and why?

Accepted Answer

The sphere, because it has a smaller moment of inertia relative to its mass and radius.

Question 9

A sound wave has an intensity of $$1.0 	imes 10$$^{-5}$$\ \mathrm{W/m}^2. $$What is the sound intensity level in decibels (dB)?

Accepted Answer

$$70\ \mathrm{dB}$$

Question 10

A $$0.2\ \mathrm{kg}$$ mass oscillates on a spring with amplitude $$0.1\ \mathrm{m}$$ and $$k = 80\ \mathrm{N/m}. $$What is the maximum kinetic energy?

Accepted Answer

$$0.4\ \mathrm{J}$$

Question 11

A train approaches a stationary observer at $$40\ \mathrm{m/s}$$, blowing its whistle at $$600\ \mathrm{Hz}. If $$the speed of sound is $$340\ \mathrm{m/s}$$, what frequency does the observer hear?

Accepted Answer

$$f' = 671\ \mathrm{Hz}$$

Question 12

A rotating object slows down from $$10\ \mathrm{rad/s} to$$ $$2\ \mathrm{rad/s} in$$ $$4\ \mathrm{s}. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = -2\ \mathrm{rad/s}^2$$

Question 13

A $$0.5\ \mathrm{kg}$$ mass on a spring oscillates with amplitude $$0.2\ \mathrm{m}$$ and $$k = 50\ \mathrm{N/m}. $$What is the total mechanical energy of the system?

Accepted Answer

$$1.0\ \mathrm{J}$$

Question 14

A river narrows from $$20\ \mathrm{m}$$ wide to $$10\ \mathrm{m}$$ wide. If the depth remains constant and the speed in the wide section is $$2\ \mathrm{m/s}$$, what is the speed in the narrow section?

Accepted Answer

$$4\ \mathrm{m/s}$$

Question 15

A $$0.3\ \mathrm{kg}$$ mass oscillates on a spring with $$k = 120\ \mathrm{N/m}. $$What is the period $$T of $$oscillation?

Accepted Answer

$$T = 1.0\ \mathrm{s}$$

Question 16

A sound wave travels from air into water. What happens to its wavelength and frequency?

Accepted Answer

Wavelength increases, frequency remains the same

Question 17

A rotating flywheel has a moment of inertia $$I = 0.2\ \mathrm{kg\cdot m^2$}$$ and angular velocity $$\omega = 5\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$2.5\ \mathrm{J}$$

Question 18

A person hears a sound at $$80\ \mathrm{dB}$$ and another at $$90\ \mathrm{dB}. $$How much more intense is the $$90\ \mathrm{dB}$$ sound compared to the $$80\ \mathrm{dB}$$ sound?

Accepted Answer

10 times more intense

Question 19

A $$0.4\ \mathrm{kg}$$ mass oscillates with amplitude $$0.15\ \mathrm{m}$$ and $$k = 100\ \mathrm{N/m}. $$What is the maximum speed?

Accepted Answer

$$1.5\ \mathrm{m/s}$$

Physics Study Notes: Rotational Motion, Fluids, Oscillations, and Sound

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