A) To find the angular velocity of the wheel in radians per second, we need to convert the given information about the time and the number of revolutions into angular units.
The formula for angular velocity is: Angular velocity (ω) = (2π * Number of revolutions) / Time
Given: Number of revolutions = 1 Time = 9 seconds
Angular velocity (ω) = (2π * 1) / 9 Angular velocity (ω) = 2π / 9 Angular velocity (ω) ≈ 0.698 radians/second (rounded to three decimal places)
Therefore, the angular velocity of the wheel is approximately 0.698 radians/second.
B) To find the linear velocity at which the hamster is running, we can use the relationship between angular velocity and linear velocity in a circular motion.
Linear velocity (v) = Radius * Angular velocity
Given: Radius of the wheel = 9 cm
Linear velocity (v) = 9 cm * 0.698 radians/second Linear velocity (v) ≈ 6.282 cm/second (rounded to three decimal places)
Therefore, the hamster is running at a linear velocity of approximately 6.282 cm/second.