If an object moves in uniform circular motion in a circle of radius R = 2.00 meters, and the object takes 5.00 seconds to complete ten revolutions, calculate the centripetal acceleration.

Hi!

The linear velocity is given by:
v = ωR

And ω is given by: ω = 2π/T (where T is the time for 1 revolution)

Now, put these equations together:
v = 2πR/T

If it takes 5 seconds for 10 revolutions, then it takes 5/10 = 0.5 seconds for each revolution.

V = (2π * 2)/0.5
V = 4π/0.5
V = 8π rad/s

Then, we goes to the centripetal acceleration:
a = V²/R
a = 64π²/2
a = 32π² rad/s²

;)

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aachen aachen · Answer 2 · 2019-10-15T05:42:00+02:00

Answer:

[tex]a=315.75\ m/s^2.[/tex]

Explanation:

Time taken to complete 10 revoution, [tex]t=5.0 \ s.[/tex]

Radius, [tex]r=2.0\ m[/tex].

We know, [tex]v=\dfrac{2\times \pi \times r}{T}[/tex].

( T is time taken to complete one revolution).

[tex]T=\dfrac{5}{10}=0.5 \ s[/tex].

[tex]v=\dfrac{2\times \pi\times 2}{0.5} \ m/s=25.13\ m/s.[/tex]

Centripetal acceleration, [tex]a=\dfrac{v^2}{r}[/tex].

Therefore, [tex]a=\dfrac{25.13^2}{2}=315.75 \ m/s^2[/tex].

Hence, it is the required solution.