a golf club 1.01 m long completes a downswing in .25s through a range of 180Degres. Assume a uniform (constant) angular velocity. What is the tangential velocity of the end of the club? What is the tangential accelration of the end of the club?
To find the tangential velocity and tangential acceleration of the end of the golf club, we need to use the formulas related to rotational motion.
1. Tangential velocity (Vt) at any point on a rotating object is given by the formula:
Vt = ω * r
where ω is the angular velocity in radians per second, and r is the distance from the axis of rotation to the point of interest.
2. Tangential acceleration (at) at any point on a rotating object is given by the formula:
at = α * r
where α is the angular acceleration in radians per second squared, and r is the distance from the axis of rotation to the point of interest.
In this scenario, we are given the following information:
- The length of the golf club (r) = 1.01 m
- The time taken for the downswing (Δt) = 0.25 s
- The range of motion (Δθ) = 180° = π radians
To find the angular velocity (ω), we can use the formula:
ω = Δθ / Δt
Calculating the angular velocity:
ω = π radians / 0.25 s
= 4π radians per second
Now we can use the given value of the distance (r = 1.01 m) and the calculated angular velocity (ω = 4π radians/s) to find the tangential velocity (Vt):
Vt = ω * r
= 4π * 1.01 m/s
≈ 12.616 m/s
So, the tangential velocity of the end of the golf club is approximately 12.616 m/s.
To find the tangential acceleration (at), you mentioned that the angular velocity is constant, which means there is no angular acceleration (α = 0). Therefore, the tangential acceleration will also be zero.
In summary:
- Tangential velocity of the end of the club = 12.616 m/s
- Tangential acceleration of the end of the club = 0 m/s²