An ice skater rotating about a vertical axis increases her angular velocity at constant rate from 7.85 rad/s to 10.65 rad/s in 2.3 s, thus her angular acceleration is 1.23 rad/s^2. During her rotation, her right leg outstretched horizontally. Calculate the radial and tangential accelerations of her skate at the end of 2.3 s. Her leg length is 90 cm.

Question

contestada

Respuesta :

CarliReifsteck CarliReifsteck · Answer 1 · 2019-09-18T16:37:22+02:00

Answer:

(a). The tangential acceleration is 1.107 m/s².

(b). The radial acceleration is 102.08 m/s².

Explanation:

Given that,

Initial angular velocity = 7.85 rad/s

Final angular velocity = 10.65 rad/s

Time = 2.3 s

Acceleration = 1.23 rad/s²

Radius = 90 cm

(a). We need to calculate the tangential acceleration

Using formula of radial acceleration

[tex]a_{t}=\alpha R[/tex]

Put the value into the formula

[tex]a_{t}=1.23\times90\times10^{-2}[/tex]

[tex]a_{t}=1.107\ m/s^2[/tex]

The tangential acceleration is 1.107 m/s².

(b). We need to calculate the radial acceleration

Using formula of radial acceleration

[tex]a_{c}=\omega^2 r[/tex]

Put the value into the formula

[tex]a_{c}=(10.65)^2\times90\times10^{-2}[/tex]

[tex]a_{c}=102.08\ m/s^2[/tex]

Hence, (a). The tangential acceleration is 1.107 m/s².

(b). The radial acceleration is 102.08 m/s².