Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg. m^2. The father exerts a force on the merry-go-round perpendicular to its radius to achieve an angular acceleration of 4.44 rad/s^2. Required:
a. How long (in s) does it take the father to give the merry-go-round an angular velocity of 1.53 rad/s? (Assume the merry-go-round is initially at rest.)
b. How many revolutions must he go through to generate this velocity?
c. If he exerts a slowing force of 270 N at a radius of 1.20 m, how long (in s) would it take him to stop them?

Explanation:

Given that:

the initial angular velocity

angular acceleration = 4.44 rad/s²

Using the formula:

Making t the subject of the formula:

where;

∴

t = 0.345 s

b)

Using the formula:

here;

= angular displacement

∴

Recall that:

2π rad = 1 revolution

Then;

0.264 rad = (x) revolution

x = 0.042 revolutions

c)

Here; force = 270 N

radius = 1.20 m

The torque = F * r

However;

From the moment of inertia;

given that;

I = 84.4 kg.m²

For re-tardation;

Using the equation

t = 0.398s

The required time it takes= 0.398s

a.) is the correct answer.

explanation:

c because the action was the roller coaster reaches bottom of hill (action) reaction would be blood tends to drain away from head

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