Answer :
A. True. Doubling radius decreases angular speed. E. True. Decreased angular speed leads to smaller angle rotated in the same time interval.
Let's analyze each option step by step:
A. The angular speed at t = 2.00 s is smaller.
- If the radius of the wheel is doubled, the angular speed will decrease. Angular speed (ω) is inversely proportional to the radius (r) of the wheel. Mathematically, ω = v/r, where v is the linear speed. Doubling the radius will halve the angular speed. So, this statement is correct.
B. The angle rotated through from t = 0 to t = 2.00 s is the same.
- The angle rotated through depends on the angular speed and the time. Since the angular speed decreases (as explained in option A), the angle rotated through will be smaller for the same time interval. So, this statement is incorrect.
C. The angle rotated through from t = 0 to t = 2.00 s is greater.
- As explained in option B, the angle rotated through will be smaller due to the decreased angular speed. So, this statement is incorrect.
D. The angular speed at t = 2.00 s is greater.
- This statement contradicts option A, which correctly states that the angular speed decreases when the radius is doubled. So, this statement is incorrect.
E. The angle rotated through from t = 0 to t = 2.00 s is smaller.
- This statement is correct. As explained in option B, the angle rotated through will be smaller due to the decreased angular speed.
F. The angular speed at t = 2.00 s is the same.
- This statement contradicts option A, which correctly states that the angular speed decreases when the radius is doubled. So, this statement is incorrect.
Therefore, options A and E are the correct answers. When the radius of the wheel is doubled, the angular speed decreases, and consequently, the angle rotated through from t = 0 to t = 2.00 s becomes smaller.
