When a rigid object rotates about a fixed axis, what is true about all the points in the object? (Select two answers.)
A) They all have the same angular speed.
B) They all have the same tangential speed.
C) They all have the same angular acceleration.
D) They all have the same tangential acceleration.
The correct answer and explanation is :
The correct answers are:
A) They all have the same angular speed.
C) They all have the same angular acceleration.
Explanation:
When a rigid object rotates about a fixed axis, every point in the object follows a circular path around that axis. There are key rotational properties that describe this motion:
- Angular Speed (ω):
- The angular speed is the rate at which the object rotates.
- Since the entire object moves as a single rigid body, all points in the object rotate through the same angle in the same time.
- This means that every point on the object has the same angular speed regardless of its distance from the axis.
- Thus, option A is correct.
- Angular Acceleration (α):
- Angular acceleration is the rate of change of angular speed.
- If the object’s rotation is speeding up or slowing down, the angular acceleration is the same for all points in the object.
- This is because each point experiences the same change in angular speed over time.
- Hence, option C is correct.
Why B and D are Incorrect:
- Tangential Speed (v = rω):
- Tangential speed depends on the radial distance (r) from the axis.
- Points farther from the axis move faster in a linear sense.
- Since r varies for different points, the tangential speed is not the same for all points.
- So, option B is incorrect.
- Tangential Acceleration (aₜ = rα):
- Like tangential speed, tangential acceleration depends on r.
- Since different points have different distances from the axis, they experience different tangential accelerations.
- Thus, option D is incorrect.