Question 1

A car is moving in a circle at constant speed. Which of the following best explains why you feel as if you are being 'thrown' outward when the car turns sharply?

Accepted Answer

Because inertia causes your body to continue moving in a straight line while the car turns, making you feel pushed outward.

Question 2

A 0.65 kg cat sits on the edge of a rotating turntable of radius $$0.75\ \mathrm{m}. If $$the coefficient of static friction between the cat and the turntable is $$\mu_s = 0.5$$, what is the maximum angular speed $$\omega (in$$ $$\mathrm{rad/s}) $$the turntable can have before the cat starts to slide?

Accepted Answer

$$\omega = \sqrt{\dfrac{\mu_s g}{r}}$$

Question 3

If the maximum static friction force is $$F_{\mathrm{fric}} = \mu_s F_N$$, what is the maximum speed $$v_{\mathrm{max}} at $$which a car can safely make a turn of radius $$r on a $$flat road?

Accepted Answer

$$v_{\mathrm{max}} = \sqrt{\mu_s g r}$$

Question 4

A bucket of water is swung in a vertical circle of radius $$0.8\ \mathrm{m}. $$What is the minimum speed at the top of the circle so that the water does not fall out?

Accepted Answer

$$v_{\mathrm{min}} = \sqrt{g r}$$

Question 5

Which of the following statements about centripetal force is correct?

Accepted Answer

Centripetal force is the net force directed toward the center of the circle, provided by other forces such as tension, gravity, or friction.

Question 6

A 2 kg object is attached to a string and swung in a horizontal circle of radius $$1.5\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = m \dfrac{v^2$}{r}$$

Question 7

A roller coaster car of mass $$500\ \mathrm{kg}$$ goes over the top of a hill of radius $$10\ \mathrm{m} at a $$speed of $$8\ \mathrm{m/s}. $$What is the normal force on the car at the top of the hill?

Accepted Answer

$$N = m g - m \dfrac{v^2$}{r}$$

Question 8

A satellite orbits Earth in a circular orbit of radius $$r. $$Which force provides the required centripetal force for its motion?

Accepted Answer

The gravitational force between the satellite and Earth.

Question 9

A 1.2 kg mass is attached to a string and whirled in a horizontal circle of radius $$0.5\ \mathrm{m} on a $$frictionless table. If the string can withstand a maximum tension of $$30\ \mathrm{N}$$, what is the maximum speed the mass can have before the string breaks?

Accepted Answer

$$v_{\mathrm{max}} = \sqrt{\dfrac{T_{\mathrm{max}} r}{m}}$$

Question 10

A car of mass $$1200\ \mathrm{kg} is $$taking a flat curve of radius $$50\ \mathrm{m} at a $$speed of $$20\ \mathrm{m/s}. If $$the coefficient of static friction is $$0.4$$, will the car skid? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Yes, because the required centripetal force exceeds the maximum frictional force.

Question 11

Which of the following best describes the direction of the acceleration of an object moving in a circle at constant speed?

Accepted Answer

It is always directed toward the center of the circle.

Question 12

A 0.5 kg mass is swung in a vertical circle of radius $$0.6\ \mathrm{m}. $$What is the tension in the string at the bottom of the circle if the speed at that point is $$3\ \mathrm{m/s}$$?

Accepted Answer

$$T = m g + m \dfrac{v^2$}{r}$$

Question 13

A 1.0 kg object moves in a circle of radius $$2.0\ \mathrm{m} at a $$constant speed of $$5.0\ \mathrm{m/s}. $$What is the magnitude of its acceleration?

Accepted Answer

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

Question 14

A 3 kg mass is attached to a string and swung in a horizontal circle of radius $$2\ \mathrm{m} at a $$speed of $$6\ \mathrm{m/s}. $$What is the net force acting on the mass?

Accepted Answer

$$F = m \dfrac{v^2$}{r}$$

Question 15

A 0.8 kg mass is attached to a string and swung in a vertical circle of radius $$1.2\ \mathrm{m}. If $$the speed at the top of the circle is $$4\ \mathrm{m/s}$$, what is the minimum tension in the string at the top?

Accepted Answer

$$T = m \dfrac{v^2$}{r} - m g$$

Physics Study Notes: Circular Motion and Forces

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