Chapter 6

Question 1

Angular speed (velocity)

Answer 1

We define angular velocity ω
as the rate of change of an angle. In symbols, this is

ω=ΔθΔt

the unit is rad/sec

Question 2

We know from kinematics that acceleration is a change in

Answer 2

velocity, either in its magnitude or in its direction, or both.

Question 3

We call the acceleration of an object moving in uniform circular motion (resulting from a net external force) the

Answer 3

centripetal acceleration

ac

Question 4

centripetal means

Answer 4

“toward the center” or “center seeking.”

Question 5

ac is proportional to

Answer 5

speed squared, implying, for example, that it is four times as hard to take a curve at 100 km/h than at 50 km/h. A sharp corner has a small radius, so that ac
is greater for tighter turns, as you have probably noticed.

Question 6

In uniform circular motion, an object moves at a constant speed, meaning the

Answer 6

magnitude of its velocity (the tangential speed) does not change. However, the direction of the velocity changes continuously as the stone moves around the circle.

Question 7

In uniform circular motion, there is a continuous change in direction of the stone’s velocity, which is caused by the

Answer 7

centripetal force. This force always acts towards the center of the circle, causing the object to continuously change its direction and move in a circular path.

Question 8

Key feature of uniform circular motion (two parts)

Answer 8

The magnitude of the velocity stays the same. The direction of the velocity is constantly changing. While an object’s speed is constant, its velocity is not constant because velocity is a vector quantity that also depends on direction. Since the direction of motion changes as an object moves around a circle, its velocity is constantly changing, even though its speed remains the same.

Question 9

In uniform circular motion, the direction of an object’s velocity continuously changes as it moves along the circular path. Therefore the object is constantly accelerating (centripetal acceleration) because the direction of its velocity is always changing, even though its speed is constant.

Answer 9

accelerating (centripetal acceleration) because the direction of its velocity is always changing, even though its speed is constant. (Is the value of “direction” always increasing? Thereby, generating a bigger and bigger number which is indicative of acceleration?)