Q: A 920 kg car travels at $$68\ \mathrm{m/s}$$ around a curve with a radius of $$75\ \mathrm{m}. $$What is the magnitude of the centripetal force required to keep the car moving in a circle?

$$F_c = \frac{mv^2$}{r} = \frac{920 \times 68^2$}{75} = 57,088\ \mathrm{N}$$

Q: A carnival ride called the Rotor has a radius of $$3.00\ \mathrm{m}$$ and completes one revolution in $$2.20\ \mathrm{s}. $$What is the linear speed of a rider?

$$v = \frac{2\pi r}{T} = \frac{2\pi \times 3.00}{2.20} = 8.57\ \mathrm{m/s}$$

Q: A person with a mass of $$75\ \mathrm{kg} is $$riding the Rotor at top speed. What is the centripetal force acting on them?

$$F_c = m a_c = 75 \times 24.5 = 1,837.5\ \mathrm{N}$$

Q: A Ferris wheel with a diameter of $$39\ \mathrm{m}$$ completes one revolution in $$8\ \mathrm{s}. $$What is the linear speed of a rider?

$$v = \frac{2\pi r}{T} = \frac{2\pi \times 19.5}{8} = 15.3\ \mathrm{m/s}$$

Question 1

Which of the following best describes the force labeled in the image above?

Accepted Answer

It is a force directed toward the center of the circle, keeping the object in circular motion.

Question 2

A 920 kg car travels at $$68\ \mathrm{m/s}$$ around a curve with a radius of $$75\ \mathrm{m}. $$What is the magnitude of the centripetal force required to keep the car moving in a circle?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{920 	imes 68^2$}{75} = 57,088\ \mathrm{N}$$

Question 3

If the centripetal force acting on an object in circular motion is suddenly removed, what path will the object follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point of release.

Question 4

A carnival ride called the Rotor has a radius of $$3.00\ \mathrm{m}$$ and completes one revolution in $$2.20\ \mathrm{s}. $$What is the linear speed of a rider?

Accepted Answer

$$v = \frac{2\pi r}{T} = \frac{2\pi 	imes 3.00}{2.20} = 8.57\ \mathrm{m/s}$$

Question 5

What is the centripetal acceleration of a rider on the Rotor described above?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{8.57^2$}{3.00} = 24.5\ \mathrm{m/s^2$}$$

Question 6

A person with a mass of $$75\ \mathrm{kg} is $$riding the Rotor at top speed. What is the centripetal force acting on them?

Accepted Answer

$$F_c = m a_c = 75 	imes 24.5 = 1,837.5\ \mathrm{N}$$

Question 7

Which of the following is NOT a source of centripetal force in real-world scenarios?

Accepted Answer

The centrifugal force acting outward on a spinning object.

Question 8

If a rider on a circular ride experiences an acceleration of $$3g$$, how heavy do they feel compared to their normal weight?

Accepted Answer

They feel three times as heavy.

Question 9

What is the period $$T of a $$rotating object, and how is it related to frequency $$f$$?

Accepted Answer

$$T is $$the time for one revolution; $$T = \frac{1}{f}$$

Question 10

A Ferris wheel with a diameter of $$39\ \mathrm{m}$$ completes one revolution in $$8\ \mathrm{s}. $$What is the linear speed of a rider?

Accepted Answer

$$v = \frac{2\pi r}{T} = \frac{2\pi 	imes 19.5}{8} = 15.3\ \mathrm{m/s}$$

Question 11

Which statement best explains why astronauts on the International Space Station (ISS) feel weightless?

Accepted Answer

They are in free fall, experiencing only centripetal acceleration.

Question 12

Which equation correctly gives the centripetal acceleration for an object moving at speed $$v in a $$circle of radius $$r$$?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 13

A circular saw blade spins at $$3600\ \mathrm{RPM}. $$What is its frequency in Hz?

Accepted Answer

$$f = \frac{3600}{60} = 60\ \mathrm{Hz}$$

Question 14

Which of the following best describes the difference between rotation and revolution?

Accepted Answer

Rotation is spinning around an internal axis; revolution is moving around an external axis.

Question 15

A merry-go-round makes one complete rotation in $$1.25\ \mathrm{s}. $$What is its speed in revolutions per minute (RPM)?

Accepted Answer

$$	ext{RPM} = \frac{60}{1.25} = 48\ 	ext{RPM}$$

Rotational Motion: Concepts, Formulas, and Applications

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