Calculating Angular Velocity of Rock Swinging in a Circle

In summary, a boy ties a 500kg rock to a 1.0m long string and swings it around his head in a horizontal circle. Using the equation sintheta = mg / T and solving for T, we get T = 28.22N. Then, using the equation v = SqRt [(rTcostheta) / m] and substituting the radius of the circle as Lcostheta, we get v = 7.4 m/s. Finally, using the equation \omega = v/r = v/(L cos (10°)), we get \omega = 7.51 rad/s. Converting to rpm, we get an angular velocity of 70.7 rpm. Overall,
  • #1
TonkaQD4
56
0
A boy ties a 500kg rock to a 1.0m long string and swings it around his head in a horizontal circle. At what angular velocity, in rpm, does the string tilt down at a 10 degree angle?

sintheta = mg / T

sin10 = 0.5kg(9.8m/s^2) / T

T = 4.9N / sin10

T = 28.22N

THEN...

v = SqRt [(rTcostheta) / m] ---> However the radius of the circle is not the length (L) so, r = Lcostheta

v = SqRt [(LTcos^2 theta) / m]

v = SqRt [(1.0m)(28.22N)(cos10^2) / 0.5kg]

v = 7.4m/s

FINALLY...

OMEGA = v / r
= v / Lcostheta

7.4rad / 1sec x 1rev / (2pi)rad x 60sec / 1 min --> rad and sec cancel out, leaving...

= 70.7 rpm


This was my initial attempt to the problem but I am not sure if everything is correct?
 
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  • #2
Looks fine through v = 7.4 m/s, but then look at [itex]\omega[/itex] = v/r = v/(L cos (10°).

cos 10° = 0.985, so [itex]\omega[/itex] = (7.4 m/s)/(0.985 m) = 7.51 rad/s

The rest is correct in form.
 
  • #3
Thanks for the correction!
 

1. How do I calculate the angular velocity of a rock swinging in a circle?

The angular velocity of a rock swinging in a circle can be calculated by dividing the angular displacement by the time taken for the rock to complete one full revolution. This can be represented by the formula ω = θ/t, where ω is the angular velocity, θ is the angular displacement, and t is the time taken.

2. What is the unit of measurement for angular velocity?

The unit of measurement for angular velocity is radians per second (rad/s). This unit represents the change in angle per unit of time.

3. How is angular velocity different from linear velocity?

Angular velocity and linear velocity are different measurements of velocity. Angular velocity measures the change in angle per unit of time, while linear velocity measures the change in distance per unit of time.

4. Can the angular velocity of a rock swinging in a circle change?

Yes, the angular velocity of a rock swinging in a circle can change if the speed or direction of the swing changes. This can also be affected by external forces such as wind or friction.

5. How can I use the angular velocity of a rock swinging in a circle in real-life applications?

The angular velocity of a rock swinging in a circle can be used in various real-life applications, such as calculating the speed of a rotating object, determining the stability of a structure, or understanding the motion of celestial bodies in space.

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