A motorcycle accelerates uniformly from rest and reaches a linear speed of 22.0 m/s in a time of 9.00s. The radius of each tire is 0.280m. What is the magnitude of the angular acceleration if each tire?
Cir. = pi * 2r = 3.14 * 0.56 = 1.76 m.
Va = 22m/s * 6.28rad/1.76m = 78.5 rad/s.
V = Vo + a*t = 78.5.
0 + a*9 = 78.5,
a = 8.72 rad/s^2.
To find the magnitude of the angular acceleration of each tire, we need to use the relationships between linear acceleration, angular acceleration, and the radius of the tire.
The linear acceleration of the motorcycle can be found using the equation:
linear acceleration = change in velocity / time
Substituting the given values:
linear acceleration = (22.0 m/s - 0 m/s) / 9.00 s
Simplifying:
linear acceleration = 22.0 m/s / 9.00 s
linear acceleration = 2.44 m/s²
The linear acceleration is also equal to the product of the angular acceleration and the radius of the tire:
linear acceleration = angular acceleration * radius
Solving for the angular acceleration:
angular acceleration = linear acceleration / radius
Substituting the values:
angular acceleration = 2.44 m/s² / 0.280 m
Simplifying:
angular acceleration = 8.71 rad/s²
Therefore, the magnitude of the angular acceleration of each tire is 8.71 rad/s².