Question

Suppose a yo-yo has a center shaft that has a 0.200 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.70 m/s2, what is the angular acceleration of the yo-yo in rad/s2? rad/s2 (b) What is the angular velocity in rad/s after 0.750 s if it starts from rest? rad/s (c) The outside radius of the yo-yo is 3.30 cm. What is the tangential acceleration in m/s2 of a point on its edge?

Answer 1

a)
`\alpha =850rad/s^2`

b)
`\omega = 637.5rad/s`

c)
`a =29.75 m/s^2`

Step-by-step explanation:

The angular acceleration is given by:

`\alpha = a/r`

`\alpha = 1.7 / 0.002`

`\alpha = 850rad/s^2`

Angular velocity is calculated by kinematics:

`\ omega = \alpha*t`

`\ omega = 850*0.75`

`\omega = 637.5rad/s`

Accelerarion on the opposite edge of the string is:

`a = \alpha*(r+R)`

`a = 850 * ( 0.002+0.033)`

`a = 29.75m/s^2`