State: the units for acceleration are?
1 answer:
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Answer:
Part 1
The angular speed is approximately 1.31947 rad/s
Part 2
The change in kinetic energy due to the movement is approximately 675.65 J
Explanation:
The given parameters are;
The rotation rate of the merry-go-round, n = 0.21 rev/s
The mass of the man on the merry-go-round = 99 kg
The distance of the point the man stands from the axis of rotation = 2.8 m
Part 1
The angular speed, ω = 2·π·n = 2·π × 0.21 rev/s ≈ 1.31947 rad/s
The angular speed is constant through out the axis of rotation
Therefore, when the man walks to a point 0 m from the center, the angular speed ≈ 1.31947 rad/s
Part 2
Given that the kinetic energy of the merry-go-round is constant, the change in kinetic energy, for a change from a radius of of the man from 2.8 m to 0 m, is given as follows;
I = m·r²
Where;
m = The mass of the man alone = 99 kg
r = The distance of the point the man stands from the axis, r = 2.8 m
v = The tangential velocity = ω/r
ω ≈ 1.31947 rad/s
Therefore, we have;
I = 99 × 2.8² = 776.16 kg·m²
= 1/2 × 776.16 kg·m² × (1.31947)² ≈ 675.65 J
Hello!
Everything you've done so far seems to be correct. However, you need to get rid of the sin. To do this, use s.
This is known as the inverse of sin, which is where you go from a fraction to the actual angle itself.
When you run through a calculator, you get about 11.537 degrees, or θ = 11.537.
To verify this, all you need to do is run sin (11.537), and the calculator returns 0.2, which is what we're looking for.
Hope this helps!