Given the radius of a wheel is 12inches and the angular speed is measured to be 3pie/4 radiant per second, find the linear speed of the piece of gum stuck to the where. Give both an exact answer. And a decimal answer rounded to 4 decimal places.
One rotation covers 2π(12) or 24π inches
in one second the wheel will cover (3π/4)÷(2π) or 3/8 of that.
(3/8) of 24π inches = 9π inches
so the linear velocity is 9π inches/sec
Use your calculator to find the decimal representation of that
348593489.1 and a half
dur ta durrr.
To find the linear speed of the piece of gum stuck to the wheel, we can use the formula:
Linear speed = Radius of the wheel x Angular speed
1. Exact Answer:
Radius of the wheel = 12 inches
Angular speed = 3π/4 radians per second
Substituting the values into the formula, we have:
Linear speed = 12 inches x (3π/4) radians per second
To get an exact answer, we'll leave the answer in terms of π without evaluating it further:
Linear speed = 36π/4 inches per second
Linear speed = 9π inches per second
Therefore, the exact linear speed of the piece of gum stuck to the wheel is 9π inches per second.
2. Decimal Answer:
To obtain a decimal approximation, we can substitute the approximate value of π, which is 3.14159, into the equation:
Linear speed = 36π/4 inches per second
Linear speed = (36 x 3.14159) / 4 inches per second
Linear speed ≈ 28.2743 inches per second
Rounded to 4 decimal places, the decimal approximation is 28.2743 inches per second.
Thus, the linear speed of the piece of gum stuck to the wheel, both in exact and decimal forms, is 9π inches per second and approximately 28.2743 inches per second, respectively.