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

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

Step-by-step 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\,(\circ)/(s)` and
`\Delta t = 3\,s`, then the change in angular position is:

`\Delta \theta = \left(30\,(\circ)/(s) \right)\cdot (3\,s)`

`\Delta \theta = 90^(\circ)`

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