a golf club 1.01 m long completes a downswing in .25s through a range of 180 degrees. Assume a uniform (constant) angular velolcity. What is the linear distance moved by the end of the club?
To find the linear distance moved by the end of the club, we need to use the concept of angular velocity and the equation that relates linear distance to angular distance.
Angular velocity is defined as the change in angular displacement over time. In this case, the angular displacement is given as 180 degrees and the time is given as 0.25 seconds. we can calculate the angular velocity as follows:
Angular velocity (ω) = angular displacement / time
ω = 180 degrees / 0.25 s
Next, we need to convert the angular displacement from degrees to radians. Since 1 radian is equal to 180 degrees / π, we can calculate the angular displacement in radians as follows:
Angular displacement (θ) = 180 degrees * (π / 180)
θ = π radians
Now we can use the equation that relates linear distance (d) to angular distance (θ) and the length of the golf club (L):
d = L * θ
Substituting the values, we get:
d = (1.01 m) * π radians
Therefore, the linear distance moved by the end of the club is approximately 3.17 meters.
distancelinear= angleinRadians*radius
= PI*1.01 meters