Q: A 1200 kg car travels around a circular path of diameter 248 meters. If $$\mu_s = 0.93$$, what is the fastest the car can move without skidding? (Use $$g = 9.8 \text{ m/s}^2)$$

$$v = \sqrt{0.93 \times 9.8 \times 124}$$

Question 1

A car travels around a flat circular track of radius $$r at $$constant speed $$v. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed the car can have without skidding?

Accepted Answer

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

Question 2

An object moves in a circle of radius $$r at $$constant speed $$v. $$What is the direction of its acceleration?

Accepted Answer

Towards the center of the circle

Question 3

A roller coaster is at the top of a circular loop. If the normal force on a passenger is $$F_N$$ and the gravitational force is $$F_g$$, what is the centripetal force acting on the passenger?

Accepted Answer

$$F_c = F_N + F_g$$

Question 4

Which of the following best describes the net force acting on an object moving at constant speed in a circular path?

Accepted Answer

The net force points towards the center of the circle.

Question 5

A planet orbits the sun in a nearly circular path. What provides the centripetal force for the planet's motion?

Accepted Answer

The gravitational force from the sun

Question 6

A rock of mass $$m is $$swung in a horizontal circle at the end of a string of length $$r. If $$the tension in the string is $$T$$, what is the correct expression for the centripetal force?

Accepted Answer

$$F_c = T$$

Question 7

If an object moves in a circle of radius $$r$$ and completes one revolution in time $$T$$, what is its speed $$v$$?

Accepted Answer

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

Question 8

A 1200 kg car travels around a circular path of diameter 248 meters. If $$\mu_s = 0.93$$, what is the fastest the car can move without skidding? (Use $$g = 9.8 	ext{ m/s}^2)$$

Accepted Answer

$$v = \sqrt{0.93 	imes 9.8 	imes 124}$$

Question 9

Which statement about centripetal force is correct?

Accepted Answer

Centripetal force is the name given to the net force pointing towards the center of a circle.

Question 10

A mass $$m$$ moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

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

Question 11

A person walks around a room in a circular path. What is the centripetal force acting on the person?

Accepted Answer

The frictional force between the person's feet and the floor

Question 12

If the net force on an object is zero, what can be said about its acceleration?

Accepted Answer

The object has zero acceleration

Question 13

A ball of mass $$m is $$attached to a string and swung in a vertical circle of radius $$r. At $$the top of the circle, what is the net force required for circular motion?

Accepted Answer

$$F_c = F_N + F_g$$

Question 14

Which of the following is NOT a requirement for an object to move in a circular path at constant speed?

Accepted Answer

Constant direction of velocity

Question 15

A mass $$m$$ moves in a circle of radius $$r$$ and period $$T. $$What is the expression for its centripetal acceleration in terms of $$r$$ and $$T$$?

Accepted Answer

$$a_c = \frac{4 \pi^2$ r}{T^2$}$$

Question 16

If the velocity of an object moving in a circle doubles, what happens to its centripetal acceleration?

Accepted Answer

It increases by a factor of 4

Question 17

A rock of mass $$m is $$swung in a horizontal circle at the end of a string of length $$r$$ with speed $$v. $$What is the tension in the string?

Accepted Answer

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

Question 18

Which of the following best explains why an object moving in a circle at constant speed is accelerating?

Accepted Answer

Its velocity vector is changing direction

Question 19

A mass $$m$$ moves in a circle of radius $$r at $$constant speed $$v. $$What is the net force acting on the mass?

Accepted Answer

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

Circular Motion: Forces, Acceleration, and Applications

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