Find the angular velocity of an object, rotating on a circular object, moving through 9.7 revolutions in 11 seconds. Express your answer in rad/sec and round your answer to the nearest tenth.
9.7 revolutions is
9.7*2*pi = 60.947 radians
Divide that by 11 s and do your own rounding.
To find the angular velocity of an object rotating on a circular path, we need to first determine the angle covered by the object in a given time.
Given that the object completes 9.7 revolutions in 11 seconds, we can determine the angle covered using the formula:
Angle (in radians) = Number of revolutions × 2π
Plugging in the given values:
Angle (in radians) = 9.7 × 2π
Now, we need to determine the time taken to cover this angle. This can be done by using the formula:
Time = Angle / angular velocity
Where angular velocity is the unknown we are trying to find.
Rearranging the formula:
Angular velocity = Angle / Time
Plugging in the known values:
Angular velocity = (9.7 × 2π) / 11
Now, let's calculate the angular velocity:
Angular velocity ≈ (9.7 × 2 × 3.14159) / 11
Angular velocity ≈ 5.56145 rad/sec
Rounding to the nearest tenth, the angular velocity of the object is approximately 5.6 rad/sec.