14. A boy is riding a bicycle at a velocity of 4 m/s. The bieycle's whel's have a diameter of 0.8
m and 40 revolutions.
a) what is the velocity of a point on the rim of the whel?
b) Calculate the angular displacement and velocity of the wheel.
c) what is the angular acceleration of a point on the rim of the wheel?
a) To find the velocity of a point on the rim of the wheel, we can use the formula for linear velocity:
linear velocity = angular velocity * radius
We know the diameter of the wheel (0.8 m), so the radius is half of that, which is 0.4 m.
linear velocity = 4 m/s (given)
radius = 0.4 m
linear velocity = angular velocity * 0.4 m
To find the angular velocity, rearrange the equation:
angular velocity = linear velocity / radius
angular velocity = 4 m/s / 0.4 m
angular velocity = 10 rad/s
Therefore, the velocity of a point on the rim of the wheel is 10 rad/s.
b) To calculate the angular displacement, we can use the formula:
angular displacement = number of revolutions * 2π radians
number of revolutions = 40 (given)
angular displacement = 40 * 2π
angular displacement = 80π radians
To find the angular velocity, we can use the formula:
angular velocity = angular displacement / time
We do not have the time given in the question, so we cannot calculate the angular velocity without that information.
c) To find the angular acceleration, we need the angular velocity and time.
angular acceleration = change in angular velocity / change in time
Since we do not have the change in time or the initial and final angular velocities, we cannot calculate the angular acceleration without that information.