Q: A car of mass 1500 kg is moving at a constant speed around a curve of radius 20 m on a flat road. If the coefficient of static friction between the tires and the road is $$\mu_s = 1.0$$, what is the maximum speed the car can have without sliding?

$$v = \sqrt{\mu_s g r} = \sqrt{1.0 \times 9.8 \times 20} = 14.0\ \mathrm{m/s}$$

Q: A table saw blade has a diameter of 25 cm and spins at 3600 rpm. What is the linear speed of a point on the edge of the blade?

$$v = 2 \pi r f = 2 \pi \times 0.125 \times 60 = 46.2\ \mathrm{m/s}$$

Q: A 7.3 kg hammer is swung in a horizontal circle at the end of a 1.2 m chain at a speed of 24 m/s. What is the tension in the chain?

$$T = m v^2$ / r = 7.3 \times 24^2$ / 1.2 = 3,504\ \mathrm{N}$$

Q: A carnival ride moves riders in a circle of radius 5 m at a speed of 8 m/s. What is the magnitude of the net force acting on a 60 kg rider?

$$F_{\text{net}} = m a = m \frac{v^2$}{r} = 60 \times \frac{8^2$}{5} = 768\ \mathrm{N}$$

Q: A car of mass $$m$$ moves at speed $$v$$ around a curve of radius $$r. $$What is the net force required to keep the car moving in a circle?

$$F_{\text{net}} = \frac{m v^2$}{r}$$

Question 1

A car of mass 1500 kg is moving at a constant speed around a curve of radius 20 m on a flat road. If the coefficient of static friction between the tires and the road is $$\mu_s = 1.0$$, what is the maximum speed the car can have without sliding?

Accepted Answer

$$v = \sqrt{\mu_s g r} = \sqrt{1.0 	imes 9.8 	imes 20} = 14.0\ \mathrm{m/s}$$

Question 2

In uniform circular motion, what is the direction of the acceleration vector at any instant?

Accepted Answer

It is directed toward the center of the circle.

Question 3

A table saw blade has a diameter of 25 cm and spins at 3600 rpm. What is the linear speed of a point on the edge of the blade?

Accepted Answer

$$v = 2 \pi r f = 2 \pi 	imes 0.125 	imes 60 = 46.2\ \mathrm{m/s}$$

Question 4

Which force provides the centripetal acceleration for a car turning a corner on a dry, flat road?

Accepted Answer

Static friction between the tires and the road.

Question 5

A 7.3 kg hammer is swung in a horizontal circle at the end of a 1.2 m chain at a speed of 24 m/s. What is the tension in the chain?

Accepted Answer

$$T = m v^2$ / r = 7.3 	imes 24^2$ / 1.2 = 3,504\ \mathrm{N}$$

Question 6

If the period of revolution for an object in uniform circular motion is $$T$$, what is its frequency $$f$$?

Accepted Answer

$$f = \frac{1}{T}$$

Question 7

A puck is tied to a string and swung in a horizontal circle on frictionless ice. What force is responsible for its centripetal acceleration?

Accepted Answer

Tension in the string.

Question 8

A car drives through a dip in the road at constant speed. At the bottom of the dip, how does the normal force of the road on the car compare to the car's weight?

Accepted Answer

The normal force is greater than the car's weight.

Question 9

Which equation correctly expresses the centripetal acceleration $$a in $$terms of speed $$v$$ and radius $$r$$?

Accepted Answer

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

Question 10

A carnival ride moves riders in a circle of radius 5 m at a speed of 8 m/s. What is the magnitude of the net force acting on a 60 kg rider?

Accepted Answer

$$F_{	ext{net}} = m a = m \frac{v^2$}{r} = 60 	imes \frac{8^2$}{5} = 768\ \mathrm{N}$$

Question 11

If a car is moving at constant speed around a circular track, which statement is true about its acceleration?

Accepted Answer

The car is accelerating because its direction is changing.

Question 12

Which of the following best explains why a car cannot turn a corner on an icy road, even if the steering wheel is turned?

Accepted Answer

There is insufficient static friction to provide the necessary centripetal force.

Question 13

What is the formula for the speed $$v of an $$object moving in a circle of radius $$r$$ with period $$T$$?

Accepted Answer

$$v = \frac{2 \pi r}{T}$$

Question 14

A car of mass $$m$$ moves at speed $$v$$ around a curve of radius $$r. $$What is the net force required to keep the car moving in a circle?

Accepted Answer

$$F_{	ext{net}} = \frac{m v^2$}{r}$$

Question 15

A car drives over a rise (a hill shaped as a circular arc) at constant speed. At the top of the rise, how does the normal force compare to the car's weight?

Accepted Answer

The normal force is less than the car's weight.

Question 16

If the frequency of rotation of an object is $$f$$, what is the formula for its centripetal acceleration $$a$$?

Accepted Answer

$$a = (2 \pi f)^2$ r$$

Question 17

A roller coaster car of mass 500 kg moves at 12 m/s through the bottom of a dip with a radius of curvature of 8 m. What is the normal force exerted by the track on the car at the bottom of the dip?

Accepted Answer

$$n = m g + m \frac{v^2$}{r} = 500 	imes 9.8 + 500 	imes \frac{144}{8} = 4,900 + 9,000 = 13,900\ \mathrm{N}$$

Question 18

Which of the following statements about apparent weight in circular motion is correct?

Accepted Answer

At the bottom of a dip, your apparent weight is greater than your true weight.

Uniform Circular Motion and Centripetal Forces: Study Notes for College Physics

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