a 10 inch radius lawn roller makes 1.2 revolutionsper second,what is angular speed in radians per second
Multiply 1.2 rev/s by 2 pi radians/revolution. The radius does not matter.
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To find the angular speed in radians per second, you need to convert the revolutions per second to radians per second.
First, let's calculate the circumference of the lawn roller. The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Where r is the radius of the circle.
Given that the radius of the lawn roller is 10 inches, we have:
Circumference = 2π * 10 = 20π inches
Now, we can convert the revolutions per second to radians per second. To do this, we need to know that 1 revolution is equal to 2π radians.
So, if the lawn roller makes 1.2 revolutions per second, the angular speed can be calculated as follows:
Angular speed = 1.2 * 2π radians per second
= 2.4π radians per second
Therefore, the angular speed of the lawn roller is 2.4π radians per second.
To find the angular speed in radians per second, we can use the formula:
Angular Speed = Linear Speed / Radius
First, we need to calculate the linear speed. The radius is given as 10 inches. The linear speed can be found by multiplying the radius by the number of revolutions per second.
Linear Speed = Radius * Revolution Per Second
Linear Speed = 10 inches * 1.2 revolutions per second
Now, let's convert the linear speed from inches per second to radians per second. Since there are 2π radians in one revolution, we can use the conversion factor:
1 revolution = 2π radians
Linear Speed (inches per second) * 2π radians/revolution = Angular Speed (radians per second)
Angular Speed = (Linear Speed * 2π) / Revolution Per Second
Now, let's substitute the values into the formula:
Angular Speed = (10 inches * 1.2 revolutions per second * 2π radians/revolution) / 1 revolution per second
Simplifying the equation:
Angular Speed = (10 inches * 1.2 * 2π) / 1
Angular Speed = 24π inches per second
Therefore, the angular speed in radians per second is 24π.