Starting from rest, a person pedals a bicycle such that the angular acceleration of the wheels is a constant 1.40 rad/s2. The bicycle wheels are 37.5 cm in radius.
(a)
What is the magnitude of the bicycle's linear acceleration (in m/s2)?
m/s2
(b)
What is the angular speed of the wheels (in rad/s) when the linear speed of the bicyclist reaches 10.0 m/s?
rad/s
(c)
How many radians have the wheels turned through in that time?
rad
(d)
How far (in m) has the bicycle traveled in that time?
m
(a) To find the magnitude of the bicycle's linear acceleration, we can use the relationship between linear and angular acceleration. The linear acceleration is given by the equation:
a = r * α
where a is the linear acceleration, r is the radius of the wheels, and α is the angular acceleration. Substituting the given values, we have:
a = (0.375 m) * (1.40 rad/s^2) = 0.525 m/s^2
Therefore, the magnitude of the bicycle's linear acceleration is 0.525 m/s^2.
(b) To find the angular speed of the wheels when the linear speed of the bicyclist reaches 10.0 m/s, we can use the relationship between linear and angular speed. The linear speed is given by the equation:
v = r * ω
where v is the linear speed, r is the radius of the wheels, and ω is the angular speed. Rearranging the equation to solve for ω, we have:
ω = v / r
Substituting the given values, we have:
ω = (10.0 m/s) / (0.375 m) = 26.67 rad/s
Therefore, the angular speed of the wheels when the linear speed of the bicyclist reaches 10.0 m/s is 26.67 rad/s.
(c) To find the number of radians the wheels have turned through in that time, we can use the relationship between angular speed and time. The angle in radians is given by the equation:
θ = ω * t
where θ is the angle in radians, ω is the angular speed, and t is the time. Rearranging the equation to solve for θ, we have:
θ = ω * t
Substituting the given values, we don't have the time t, so we cannot determine the number of radians the wheels have turned through without that information.
(d) To find how far the bicycle has traveled in that time, we can use the relationship between linear speed and time. The distance traveled is given by the equation:
d = v * t
where d is the distance traveled, v is the linear speed, and t is the time. Rearranging the equation, we have:
t = d / v
Substituting the given values, we don't have the time t, so we cannot determine the distance the bicycle has traveled without that information.