Multiple-Concept Example 8 provides some pertinent background for part (b) of th

Question

Multiple-Concept Example 8  provides some pertinent background for part (b) of this problem. A motorcycle, which has an initial linear speed of 6.8   m/s, decelerates to a speed of 1.7  m/s in 5.0 s. Each wheel has a radius of 0.62  m and is rotating in a counterclockwise (positive) directions. What is (a) the constant angular acceleration (in rad/s2) and (b) the angular displacement (in rad) of each wheel?

Multiple-Concept Example 8:

Multiple-Concept Example 8 provides some pertinent background for part (b) of this problem. A motorcycle, which has an initial linear speed of 6.8 m/s, decelerates to a speed of 1.7 m/s in 5.0 s. Each wheel has a radius of 0.62 m and is rotating in a counterclockwise (positive) directions. What is (a) the constant angular acceleration (in rad/s2) and (b) the angular displacement (in rad) of each wheel? Multiple-Concept Example 8: An automobile, starting from rest, has a linear acceleration to the right whose magnitude is. During the next 20.0 s, the tires roll and do not slip. The radius of each wheel is 0.330 m. At the end of this time, what is the angle through which each wheel has rotated? Algebraically combining the results of the modeling steps, we have: The angle through which each wheel rotates is The minus sign in this result means that the wheel has rotated in the clockwise direction.

Explanation / Answer

Radius r = .62 m
Initial linear speed vo =6.8 m/s
Final linear speed v = 1.7m/s
Time t = 5.0 s

Linear acceleration a = (v - vo)/t = (1.7 - 6.8)/5.0 =-1.02 m/s
Angular acceleration = a/r = --1.02/0.62 = --1.645161290322581 rad/s^2

Linear displacement S = (v + vo) * t/2 = (1.7 + 6.8) * 5.0/2 = 21.25 m
Angular displacement = S/r = 21.25/0.62 = 34.2741935483871rad

Ans: (a)--1.645161290322581 rad/s^2 (b)34.2741935483871rad

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