Lance Deal's Angular Velocity & Centripetal Force in Rotational Motion

In summary, Lance Deal launched the hammer 81.12m, winning a silver medal at the Atlanta Olympics. The hammer, which is thrown by rotating the body in a circle, has a radius of rotation of 2.00m and is launched at an angle of 35.0 degrees to the horizontal with a velocity of 28.8m/s. Lance's angular velocity at release was 14.4 rad/s and the centripetal force he exerted on the 7.26kg hammer was 3.01 x 10^3N. If holding the hammer in your hand, it would feel like a mass of 307kg due to the equivalent force.
  • #1
faoltaem
31
0
On his last throw of the Atlanta Olympics, Lance Deal launched the hammer 81.12m, good enough for a silver medal. The hammer is thrown by rotating the body in a circle, building up rotational speed until releasing it and letting the rotational velocity change to translational velocity. The hammer is affixed on the end of a 1.21m long cord and along with the arms makes for a radius of rotation of 2.00m. Knowing that the hammer is launched at an angle of 35.0 degrees to the horizontal, we can use projectile motion equations to calculate that the hammer is launched with a velocity of 28.8m/s.
a) What is Lance Deal’s angular velocity as he releases the hammer?
b) The ball of the hammer weighs 7.26kg. What centripetal force was Lance exerting to hold onto the hammer?
c) Convert the centripetal force to its equivalent in mass if you were holding it in your hand.


Homework Equations


[tex]v = r\omega[/tex]

[tex]\frac{\Delta\omega}{\Delta t}[/tex]

[tex]\omega = \frac{d}{\Delta t}[/tex]

[tex]\overline{\alpha} = \frac{\Delta\omega}{\Delta t}[/tex]

[tex]a_{cp}=r\omega^{2}[/tex]

[tex]w_{f}^{2} = w_{o}^{2} + 2\alpha\theta[/tex]

[tex]v_{f}^{2} = v_{o}^{2} + 2ax[/tex]

The Attempt at a Solution


i'm finding it a little bit hard to get started on this question because all of the relavent equations that i have either have time or a form of acceleration in them and i haven't been given either of these. would it be possible for someone to tell me what equation they would use for (a), and then i should be able to work them all out cause the questions are kind of flow on.
 
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  • #2
Hi

You already wrote down more equations than needed.

a) [tex]v=r*\omega \Rightarrow \omega=\frac{v}{r}[/tex] with given velocity v (=28.8 m/s) and r (=2m) you can easily calculate the angular velocity [tex]\omega[/tex],

b) Centripetal force [tex]F_{z}=\frac{m*v^{2}}{r}=m*r*\omega^{2}[/tex]

I hope this helps you a bit...

Yannick
 
  • #3
thanks i didn't realized i'd overlooked that information

so:
a) [tex]\omega = \frac{v}{r} = \frac{28.8}{2}[/tex] = [tex]\underline{14.4rad/s}[/tex]

b) [tex]f_cp = ma_cp = \frac{mv^{2}}{r} = mr\omega^{2}[/tex]
= 7.26 x 2 x 14.4[tex]^{2}[/tex]
=3010.8672 = [tex]\underline{3.01 x 10^{3}N}[/tex]

c) F=mg F=[tex]f_cp[/tex] = 3011N, g=9.81m/s[tex]^{2}[/tex]

[tex]m=\frac{F}{g} = \frac{3011}{9.81}[/tex] = 306.918
=[tex]\underline{307kg}[/tex]
 

1. What is angular velocity and how is it related to rotational motion?

Angular velocity is a measure of how quickly an object is rotating around a fixed point or axis. It is typically represented by the symbol ω (omega) and is measured in radians per second. Angular velocity is directly related to rotational motion because it describes the rate of change of an object's angular position over time.

2. What is the formula for calculating angular velocity?

The formula for angular velocity is ω = Δθ/Δt, where ω is angular velocity, Δθ represents the change in angular position, and Δt is the change in time. This formula can also be expressed as ω = 2πf, where f is the frequency of rotation in revolutions per second.

3. How does angular velocity differ from linear velocity?

Angular velocity and linear velocity are both measures of how fast an object is moving, but in different ways. Angular velocity describes the rate of rotation around an axis, while linear velocity describes the rate of change of an object's linear position. Angular velocity is also measured in radians per second, while linear velocity is typically measured in meters per second.

4. What is centripetal force and how does it relate to rotational motion?

Centripetal force is a force that acts towards the center of a circular motion and keeps an object moving in a circular path. It is necessary for an object to maintain uniform circular motion, as it counteracts the centrifugal force that pulls an object away from the center of rotation. In rotational motion, centripetal force is responsible for keeping an object moving in a circular path and creating the necessary centripetal acceleration.

5. How can we apply the concepts of angular velocity and centripetal force in real-world situations?

Angular velocity and centripetal force are important concepts in many real-world situations, such as amusement park rides, car racing, and satellite orbits. Understanding these concepts allows us to calculate the necessary forces and velocities to keep objects moving in circular paths and prevent accidents or failures. They are also important in designing and analyzing rotating machinery and structures.

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