Q: At the top of a vertical circle, what is the minimum speed $$v_{\text{min}}$$ required for an object to remain in circular motion?

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

Question 1

In non-uniform circular motion, which component of the net force is responsible for changing the speed of the object?

Accepted Answer

The tangential component

Question 2

A ball of mass $$m$$ rolls counterclockwise inside a horizontal pipe of radius $$r. $$What is the instantaneous angular acceleration $$\alpha at $$the point shown if gravity acts downward?

Accepted Answer

$$\alpha = -\frac{g}{r}$$

Question 3

An object is swung in a vertical circle on the end of a string. When the object is at the bottom of the circle, the tension in the string is:

Accepted Answer

Greater than the weight of the object

Question 4

At the top of a vertical circle, what is the minimum speed $$v_{	ext{min}}$$ required for an object to remain in circular motion?

Accepted Answer

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

Question 5

A bucket is swung in a vertical circle. At the top of the circle, what force prevents the contents from falling out?

Accepted Answer

Gravity

Question 6

A 500 g rocket is attached to a pivot in the center of a flat table. The rocket provides a thrust force of 3 N at an angle $$\phi = 70^\circ. $$What is the radial component of the thrust force?

Accepted Answer

1.0 N

Question 7

For the same rocket, what is the tangential (linear) acceleration $$a_t$$?

Accepted Answer

1.4 $$m/s^2$$

Question 8

A 500 g rocket is attached to a pivot and provides a thrust force of 3 N at $$\phi = 70^\circ. $$What is the rocket’s angular velocity $$\omega$$ after 5 seconds of thrust?

Accepted Answer

14 rad/s

Question 9

A 500 g rocket is attached to a pivot and provides a thrust force of 3 N at $$\phi = 70^\circ. $$What is the tension in the rod after 5 seconds of thrust?

Accepted Answer

196 N

Question 10

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

Accepted Answer

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

Question 11

If the net force on an object in circular motion is not entirely radial, what happens to the object’s motion?

Accepted Answer

The object’s speed changes

Question 12

A roller coaster car goes around a loop-the-loop. If its speed at the top is less than the critical speed, what will happen?

Accepted Answer

It will fall off the circular path

Question 13

Which of the following best describes the relationship between tangential acceleration $$a_t$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$a_t = r \alpha$$

Question 14

A car is moving in a vertical circle. At the top of the circle, the normal force is zero. What is the speed of the car?

Accepted Answer

$$v = \sqrt{g r}$$

Question 15

Which force is always directed toward the center of the circle in circular motion?

Accepted Answer

Centripetal force

Question 16

A ball is rolling inside a horizontal pipe. If the net force has both radial and tangential components, what is true about its motion?

Accepted Answer

The ball’s speed increases or decreases

Question 17

If the tension in a string is less than zero at the top of a vertical circle, what does this imply?

Accepted Answer

The string is slack and cannot maintain circular motion

Question 18

A rocket provides a thrust force at an angle. Which component of the force is responsible for changing the rocket’s angular velocity?

Accepted Answer

Tangential component

Question 19

Which of the following is a real-world example of the critical speed concept in vertical circular motion?

Accepted Answer

A roller coaster going around a loop-the-loop

Question 20

In the context of circular dynamics, what is the primary difference between uniform and non-uniform circular motion?

Accepted Answer

Uniform motion has constant speed; non-uniform motion has changing speed

Circular Dynamics and Non-Uniform Circular Motion: Study Notes

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