Suppose a yo-yo has a center shaft that has a 0.250 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 1.50 m/s2, what is the angular acceleration of the yo-yo?
(b) what is the angular velocity after 0.750 s if it starts from rest?
(c) the outside radius of the yo-yo is 3.50 cm. what is the tangential acceleration of a point on its edge? ans:

(a) 600 rad/s2,
(b) 450 rad/s,
(c) 21.0 m/s

600 rad/s²

450 rad/s

21 m/s²

Explanation:

r = Radius

= Final angular velocity

= Initial angular velocity

= Angular acceleration

t = Time taken

Linear acceleration is given by

Angular acceleration of the yo-yo is 600 rad/s²

angular velocity of the yo-yo is 450 rad/s

Tangential acceleration of a point on its edge is 21 m/s²

1) Yes

2)

Explanation:

1)

To solve this part, we have to calculate the pressure at the depth of the batyscaphe, and compare it with the maximum pressure that it can withstand.

The pressure exerted by a column of fluid of height h is:

where

is the atmospheric pressure

is the fluid density

is the acceleration due to gravity

h is the height of the column of fluid

Here we have:

is the sea water density

h = 5440 m is the depth at which the bathyscaphe is located

Therefore, the pressure on it is

Since the maximum pressure it can withstand is 60 MPa, then yes, the bathyscaphe can withstand it.

2)

Here we want to find the force exerted on the bathyscaphe.

The relationship between force and pressure on a surface is:

where

p is hte pressure

F is the force

A is the area of the surface

Here we have:

is the pressure exerted

The bathyscaphe has a spherical surface of radius

r = 3 m

So its surface is:

Therefore, we can find the force exerted on it by re-arranging the previous equation: