A wheel has a radius of 2.2 m.
How far (path length) does a point on the
circumference travel if the wheel is rotated
through an angle of 190 rad?
Answer in units of m
Distance S = R*(theta)
Use that formula to compute the distance yourself.
"theta" is the angle in radians, which you have been given. The wheel obviously makes many revolutions. 190/(2 pi) = 30.239 revolution.
To find the distance traveled by a point on the circumference of a wheel, we need to calculate the circumference of the wheel and then multiply it by the angle of rotation.
Step 1: Calculate the circumference of the wheel.
The circumference of a wheel is given by the formula C = 2πr, where r is the radius of the wheel. In this case, the radius is given as 2.2 m.
So, the circumference of the wheel is C = 2π(2.2) = 4.4π m (using the value of π as approximately 3.14).
Step 2: Multiply the circumference by the angle of rotation.
The distance traveled by a point on the circumference is given by the formula d = Cθ, where d is the distance traveled and θ is the angle of rotation in radians. In this case, the angle of rotation is given as 190 rad.
So, the distance traveled is d = (4.4π)(190) ≈ 8336.8 m (approximating π as 3.14).
Therefore, a point on the circumference of the wheel travels approximately 8336.8 meters.