Question

1.) You whirl a stone in a horizontal circle in such a way that the stone is in uniform circular motion. Which of the following is true for this situation? (Select all that apply.)

The change in direction of the stone's motion is due to the centripetal force acting on the stone.

The direction of the stone's velocity changes as it moves around the circle.

The stone is moving with constant velocity.

The stone's speed is constant.

The magnitude of the stone's velocity does not change.

2.) Consider different points along one spoke of a wheel rotating with constant angular velocity. Which of the following is true regarding the centripetal acceleration at a particular instant of time?
Both the magnitude and the direction of the centripetal acceleration depend on the location of the point on the spoke.

The magnitude and direction of the centripetal acceleration is the same at all points on this spoke.     

The magnitude of the centripetal acceleration is smaller for points on the spoke closer to the hub than for points closer to the rim but the direction of the acceleration is the same at all points on this spoke.

The magnitude of the centripetal acceleration is greater for points on the spoke closer to the hub than for points closer to the rim. (Not Correct)

Answer 1

1) The following are true:

The change in direction of the stone's motion is due to the centripetal force acting on the stone.

The direction of the stone's velocity changes as it moves around the circle.

The stone's speed is constant.

The magnitude of the stone's velocity does not change.

These are because the centripetal acceleration acts perpendicular to the velocity, so it doesn't change the magnitude of the velocity, but alters its direction. Also, speed is simply the absolute value of velocity, as there is no direction associated with it. Therefore, speed is constant, but velocity isn't, as direction changes.

2) Only this is true: The magnitude of the centripetal acceleration is smaller for points on the spoke closer to the hub than for points closer to the rim but the direction of the acceleration is the same at all points on this spoke.

Using a = w^2 * r, we see that as r increases, the centripetal acceleration increases.

Answer 2

1)

The change in direction of the stone's motion is due to the centripetal force acting on the stone.

The direction of the stone's velocity changes as it moves around the circle.

The stone's speed is constant.

The magnitude of the stone's velocity does not change.

2)

The magnitude of the centripetal acceleration is smaller for points on the spoke closer to the hub than for points closer to the rim but the direction of the acceleration is the same at all points on this spoke.

Answer 3

1) a,b,c,e
2) Ac = r*w

Answer 4

1) all are true

2) 3rd option is correct