Final answer:
The angular velocity of a 1.3-kg solid sphere rotating about its diameter at 78 rev/min is approximately 8.17 rad/s.
Step-by-step explanation:
The angular velocity of a rotating object can be calculated using the formula:
angular velocity = (2π × number of revolutions)/(time in seconds)
In this case, the object is a solid sphere with a mass of 1.3 kg and a diameter of 14 cm. Since it is rotating about its diameter, we know that the radius is half the diameter, which is 7 cm. To find the number of revolutions per second, we divide the given value of 78 rev/min by 60 to convert it to rev/s. Plugging in the values, we get:
angular velocity = (2π × 78 rev/s)/(60 s) ≈ 8.17 rad/s