A golf club 1.01 m long completes a downswing in 0.25 s through a range of 180°. Assume a uniform (constant) angular velocity, what is the average angular velocity of the club?
I don't even know what equation to begin with.
To find the average angular velocity, we need to find the change in the angular displacement (Δθ) and the time interval (Δt) over which this change occurred. The equation for average angular velocity is given by:
Average angular velocity (ω_avg) = Δθ / Δt
Now, let's break down the problem to find the values we need for this equation.
The golf club completes a swing through a range of 180°. In other words, the change in angular displacement (Δθ) is equal to 180°.
The time taken for the downswing is given as 0.25 seconds, so the time interval (Δt) is also 0.25 s.
Now, we can substitute these values into the equation:
ω_avg = Δθ / Δt
ω_avg = 180° / 0.25 s
However, it is important to note that angular velocity should be in radians per second (rad/s) instead of degrees per second (°/s). To convert degrees to radians, we use the conversion factor:
1 radian = (π/180) degrees
So, we can convert the unit as follows:
ω_avg = (180° * π/180) / 0.25 s
ω_avg = π rad / 0.25 s
Therefore, the average angular velocity of the golf club is π rad/s.
Note: π is approximately 3.14, so the average angular velocity would be approximately 3.14 rad/s.
pi radians divided by 0.25 s = 4 pi rad/s
The length of the golf club does not matter.