A wheel rotates with a constant angular acceleration of 3.50 rad/s2. The angular speed of the wheel is 2.00 rad/s at t = 0. If the radius of the wheel is doubled, Are the following statements affected? If so, in what way? (Select all that apply.)

(1)The angular speed at t = 2.00 s is the same.
(2) The angle rotated through from t = 0 to t = 2.00 s is smaller.
(3) The angle rotated through from t = 0 to t = 2.00 s is the same.
(4) The angular speed at t = 2.00 s is greater.
(5)The angle rotated through from t = 0 to t = 2.00 s is greater.
(6)The angular speed at t = 2.00 s is smaller.

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i think its (4) and (5) but i have no clue...
Thank You

I figured it out!!

It was (1) and (3)
Never mind!

Yes, 1 and 3.

To determine which statements are affected, we can investigate the effect of doubling the radius on the angular acceleration and angular speed of the wheel.

Let's analyze each statement one by one:

(1) The angular speed at t = 2.00 s is the same.

This statement is true. The angular speed depends on the angular acceleration and time, but doubling the radius does not affect the angular acceleration. Therefore, the angular speed at t = 2.00 s will remain the same.

(2) The angle rotated through from t = 0 to t = 2.00 s is smaller.

This statement is false. The angle rotated depends on the angular acceleration, angular speed, and time. While doubling the radius does not affect the angular acceleration, it does affect the angular speed. As a result, the wheel will rotate through a larger angle in the same time interval, making this statement incorrect.

(3) The angle rotated through from t = 0 to t = 2.00 s is the same.

This statement is false. As mentioned in statement (2), doubling the radius will result in a larger angle being rotated in the given time interval. Therefore, the angle rotated from t = 0 to t = 2.00 s will be greater, not the same.

(4) The angular speed at t = 2.00 s is greater.

This statement is true. Doubling the radius of the wheel will result in a larger angular speed at any given time. Therefore, the angular speed at t = 2.00 s will be greater.

(5) The angle rotated through from t = 0 to t = 2.00 s is greater.

This statement is true. As mentioned in statements (2) and (3), doubling the radius will cause the wheel to rotate through a larger angle within the same time interval. Therefore, the angle rotated from t = 0 to t = 2.00 s will be greater.

(6) The angular speed at t = 2.00 s is smaller.

This statement is false. Doubling the radius of the wheel will result in a larger angular speed at any given time. Therefore, the angular speed at t = 2.00 s will be greater, not smaller.

So, the correct statements are:
(1) The angular speed at t = 2.00 s is the same.
(4) The angular speed at t = 2.00 s is greater.
(5) The angle rotated through from t = 0 to t = 2.00 s is greater.

I hope this explanation clarifies things for you!

To determine how changing the radius of the wheel will affect the statements, let's analyze the situation step by step.

First, let's find the angular speed at t = 2.00 s using the given information. We know the initial angular speed (ω0) is 2.00 rad/s, the angular acceleration (α) is 3.50 rad/s^2, and the time (t) is 2.00 s. We can use the following kinematic equation:

ω = ω0 + αt

Substituting the given values:

ω = 2.00 rad/s + (3.50 rad/s^2)(2.00 s)
ω = 2.00 rad/s + 7.00 rad/s
ω = 9.00 rad/s

Now, let's consider how the changes in the radius will affect the statements:

(1) The angular speed at t = 2.00 s is the same.
This statement is NOT affected by the change in radius. The angular speed at t = 2.00 s is solely determined by the initial angular speed and the angular acceleration, not by the radius. Therefore, the angular speed at t = 2.00 s remains 9.00 rad/s regardless of the radius change.

(2) The angle rotated through from t = 0 to t = 2.00 s is smaller.
This statement is NOT affected by the change in radius. The angle rotated through is determined by the angular speed and the time interval, not by the radius. Therefore, the angle rotated through from t = 0 to t = 2.00 s remains the same regardless of the radius change.

(3) The angle rotated through from t = 0 to t = 2.00 s is the same.
This statement is correct. Since the angle rotated through is determined by the angular speed and the time interval, which are unaffected by the radius change, the angle will remain the same.

(4) The angular speed at t = 2.00 s is greater.
This statement is correct. As calculated earlier, the angular speed at t = 2.00 s is 9.00 rad/s. Therefore, the angular speed at t = 2.00 s is greater regardless of the radius change.

(5) The angle rotated through from t = 0 to t = 2.00 s is greater.
This statement is NOT affected by the change in radius. The angle rotated through is determined by the angular speed and the time interval, not by the radius. Therefore, the angle rotated through from t = 0 to t = 2.00 s remains the same regardless of the radius change.

(6) The angular speed at t = 2.00 s is smaller.
This statement is NOT affected by the change in radius. As calculated earlier, the angular speed at t = 2.00 s is 9.00 rad/s and remains the same regardless of the radius change.

So, the correct statements are:
(3) The angle rotated through from t = 0 to t = 2.00 s is the same.
(4) The angular speed at t = 2.00 s is greater.