Answer:
3.229 revolutions per minute
Explanation:
The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.
To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.
The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.
To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.
In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.
Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.
Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.
Angular velocity = linear velocity / distance traveled in one revolution
Angular velocity = 17 centimeters per second / (20π centimeters per revolution)
Simplifying the expression, we get:
Angular velocity = 17 / (20π) revolutions per second
To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).
Angular velocity in revolutions per minute = (17 / (20π)) * 60
Calculating the value, we get:
Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute
Therefore, the wheel will s
AI-generated answer
The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.
To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.
The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.
To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.
In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.
Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.
Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.
Angular velocity = linear velocity / distance traveled in one revolution
Angular velocity = 17 centimeters per second / (20π centimeters per revolution)
Simplifying the expression, we get:
Angular velocity = 17 / (20π) revolutions per second
To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).
Angular velocity in revolutions per minute = (17 / (20π)) * 60
Calculating the value, we get:
Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute
Therefore, the wheel will spin at a rate of approximately 3.229 revolutions per minute.