14. A boy is riding a bicycle at a velocity of 4 m/s. The bieycle's whel's have a diameter of 0.8m 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) The velocity of a point on the rim of the wheel can be calculated using the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel. Since the diameter of the wheel is 0.8m, the radius (r) is half of the diameter, which is 0.4m. The angular velocity (ω) can be calculated by dividing the linear velocity (v) by the radius (r):
ω = v / r = 4 m/s / 0.4 m = 10 rad/s
b) The angular displacement (θ) of the wheel can be calculated using the formula:
θ = number of revolutions * 2π
Since there are 40 revolutions, the angular displacement is:
θ = 40 * 2π = 80π rad
The angular velocity (ω) of the wheel is constant and can be calculated by dividing the angular displacement (θ) by the time taken (t):
ω = θ / t
Since no time is given in the question, we cannot calculate the angular velocity.
c) The angular acceleration (α) of a point on the rim of the wheel can be calculated using the formula:
α = (ωf - ωi) / t
where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time taken. Since time is not given in the question, we cannot calculate the angular acceleration.