Question

A spinning disk is rotating at a rate of 3 rad/s in the positive counterclock-wise direction. if the disk is subjected to an angular acceleration in the clock-wise direction at a rate of 4 rad/s² , find the wheel's angular velocity in rad/s after 2 s.

a. -5 rad/s.
b. -11 rad/s.
c. 8 rad/s.
d. 5 rad/s.
e. -8 rad/s.

Answer 1

The disk's angular velocity after 2 seconds, given the initial condition and angular deceleration applied, is -5 rad/s. This indicates that the disk is rotating in the clockwise direction at that rate.

Step-by-step explanation:

To find the disk's angular velocity after 2 seconds, we need to consider the initial angular velocity and the angular acceleration applied in the opposite direction. The equation needed to find the final angular velocity (\(\omega_f\)) when an angular acceleration (\(\alpha\)) is applied over a time period (t) is:

\(\omega_f = \omega_i + \alpha * t\)

Where:

• \(\omega_i\) = Initial angular velocity = 3 rad/s (positive indicates counterclockwise direction)
• \(\alpha\) = Angular acceleration = -4 rad/s² (negative indicates clockwise direction)
• t = Time = 2 s

Plugging in the values, we get:

\(\omega_f = 3 rad/s + (-4 rad/s² * 2 s)\)

\(\omega_f = 3 rad/s - 8 rad/s\)

\(\omega_f = -5 rad/s\)

Therefore, the angular velocity of the disk after 2 seconds will be -5 rad/s, which means it will be rotating in the clockwise direction at that rate.