Before throwing a 0.821 kg discus, an athlete rotates it along a circular path of radius
1.19 m. The maximum speed of the discus is 18.7 m/s.
Determine the magnitude of its maximum
radial acceleration.
Answer in units of m/s2.
radial acceleration= v^2/r
To determine the magnitude of the maximum radial acceleration of the discus, we can start by understanding the relationship between radial acceleration, rotational speed, and radius.
The formula for radial acceleration is given by:
a_radial = v^2 / r
Where:
- a_radial is the radial acceleration
- v is the linear speed or velocity
- r is the radius of the circular path
In this case, we are given the linear speed of the discus, which is its maximum speed, v = 18.7 m/s, and the radius of the circular path, r = 1.19 m.
Substituting these values into the formula, we can calculate the magnitude of the maximum radial acceleration:
a_radial = (18.7 m/s)^2 / 1.19 m
Simplifying the calculation:
a_radial = 348.69 m^2/s^2 / 1.19 m
a_radial ≈ 292.70 m/s^2
Therefore, the magnitude of the maximum radial acceleration of the discus is approximately 292.70 m/s^2.