Question

A disk rotates at a constant angular velocity of 30 degrees per second. Consider a point on the edge of the disk. Through how many degrees has it rotated after 3 seconds?

Answer 1

Answer:

The disk covers a rotation of 90º after 3 seconds.

Explanation:

Since the disk rotates at constant angular speed, we can determine the change in angular position ($\Delta \theta$), measured in sexagesimal degrees, by the following kinematic formula:

$\Delta \theta = \omega\cdot \Delta t$ (1)

Where:

$\omega$ - Angular velocity, measured in sexagesimal degrees per second.

$\Delta t$ - Time, measured in seconds.

If we know that $\omega= 30\,\frac{\circ}{s}$ and $\Delta t = 3\,s$, then the change in angular position is:

$\Delta \theta = \left(30\,\frac{\circ}{s} \right)\cdot (3\,s)$

$\Delta \theta = 90^{\circ}$

The disk covers a rotation of 90º after 3 seconds.