A spinning disk is rotating at a rate of 4 rad/s in the counterclockwise directi

Question

A spinning disk is rotating at a rate of 4 rad/s in the counterclockwise direction as shown in the figure.
What is the direction of the angular velocity vector?

Incorrect down
Incorrect right
Correct: up
Incorrect left

If the disk is speeding up at a rate of 4 rad/s2, what is the direction of the angular acceleration vector?

Incorrect down
Incorrect right
Correct: up
Incorrect left

Find the wheel's angular velocity after 4 s.
rad/s

Find the angle through which the wheel has turned after 4 s in radians.
radians

Find the magnitude of the velocity (speed) of a point located at r = 20 cm from the center of the wheel after 4 s.
m/s

Find the magnitude of the parallel acceleration of the point in the above part.
m/s2

Explanation / Answer

1) Remember to wrap your right hand in the direction of rotation and your thumb will give the direction of the angular velocity. Ans: UP

2) It will be same to the angular velocity vector because it is speeding up.  Ans: UP

3) ? = ?o+ ?t = 4 + (4*4) = 4 + 16 = 20 rad/s

4) Remember that the angle is given by: ? = ?o + ?o*t + 0.5?t²

? = 0 + 4*4 + 0.5*4*16 = 48 rad

5) Remember that the linear velocity v = r?.

v = (0.2m * 20 rad/s) ==> 4 m/s

6) Remember that the parallel acceleration a = r? = 0.2*4 = 0.8 m/s^2

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