Question

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.

Answer 1

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

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

Step-by-step 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

`a_(t)=\alpha R`

Put the value into the formula

`a_(t)=1.23*90*10^(-2)`

`a_(t)=1.107\ m/s^2`

The tangential acceleration is 1.107 m/s².

(b). We need to calculate the radial acceleration

Using formula of radial acceleration

`a_(c)=\omega^2 r`

Put the value into the formula

`a_(c)=(10.65)^2*90*10^(-2)`

`a_(c)=102.08\ m/s^2`

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

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