Question 1

Which of the following statements about uniform circular motion (UCM) is correct?

Accepted Answer

The object experiences acceleration because its velocity changes direction, even though its speed is constant.

Question 2

A ball is spun on a string in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the formula for the period $$T of $$one revolution?

Accepted Answer

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

Question 3

What is the direction of the centripetal acceleration for an object in uniform circular motion?

Accepted Answer

Inward, toward the center of the circle

Question 4

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

Accepted Answer

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

Question 5

A car of mass $$m$$ moves at constant speed $$v$$ around an unbanked curve of radius $$r. If $$the only radial force is friction, what is the maximum speed $$v_{max}$$ the car can have without sliding, given the coefficient of static friction $$\mu_s$$?

Accepted Answer

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

Question 6

Why does the sensation of being 'thrown outward' in a turning car not represent a real force according to Newton's laws?

Accepted Answer

Because it is a fictitious force that arises in a non-inertial reference frame.

Question 7

A ball of mass $$m is $$twirled in a horizontal circle of radius $$r at $$speed $$v. $$What is the tension $$T in $$the string if the ball is moving in uniform circular motion?

Accepted Answer

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

Question 8

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

Accepted Answer

The gravitational force between the Earth and the satellite

Question 9

Which equation gives the radius $$r of a $$satellite's circular orbit around Earth in terms of its orbital speed $$v$$, Earth's mass $$M$$, and the gravitational constant $$G$$?

Accepted Answer

$$r = \dfrac{G M}{v^2$}$$

Question 10

A geosynchronous satellite orbits Earth with a period of 24 hours. What must be true about its orbital radius compared to satellites with shorter periods?

Accepted Answer

It must be larger than satellites with shorter periods.

Question 11

An astronaut in the International Space Station appears weightless because:

Accepted Answer

The astronaut and the station are both in free fall, accelerating at the same rate.

Question 12

To create 'artificial gravity' in a rotating space station, what must be true about the motion of the station?

Accepted Answer

The station must rotate so that the centripetal acceleration at the rim equals Earth's gravity.

Question 13

A motorcycle performs a vertical loop-the-loop. At the top of the loop, what is the minimum speed $$v_{min}$$ required to stay in contact with the track?

Accepted Answer

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

Question 14

During NASA's 'Vomit Comet' parabolic flight, passengers experience weightlessness at the top of the trajectory because:

Accepted Answer

The plane and passengers are both in free fall, accelerating downward at $$g.$$

Question 15

If the tension in the string twirling a ball in a horizontal circle is suddenly cut, what path will the ball follow?

Accepted Answer

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

Question 16

Which of the following is true about the centripetal force in circular motion?

Accepted Answer

It is the vector sum of all radial forces acting toward the center.

Question 17

A ball on a string is twirled in a horizontal circle. If the speed is doubled, by what factor does the required tension in the string change?

Accepted Answer

It quadruples.

Question 18

A satellite orbits Earth at radius $$r$$ with speed $$v. If $$the speed is increased, what happens to the radius of the orbit required to maintain a circular path?

Accepted Answer

The radius must decrease.

Question 19

Which of the following best explains why Newton's laws are only valid in inertial reference frames?

Accepted Answer

Because fictitious forces, like centrifugal force, appear in non-inertial frames.

Uniform Circular Motion and Centripetal Forces: Study Notes

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