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

[faoltaem]

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

$$v = r\omega$$

$$\frac{\Delta\omega}{\Delta t}$$

$$\omega = \frac{d}{\Delta t}$$

$$\overline{\alpha} = \frac{\Delta\omega}{\Delta t}$$

$$a_{cp}=r\omega^{2}$$

$$w_{f}^{2} = w_{o}^{2} + 2\alpha\theta$$

$$v_{f}^{2} = v_{o}^{2} + 2ax$$

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.

 

[Yannick]

Hi

You already wrote down more equations than needed.

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

b) Centripetal force $$F_{z}=\frac{m*v^{2}}{r}=m*r*\omega^{2}$$

I hope this helps you a bit...

Yannick

 

[faoltaem]

thanks i didn't realized i'd overlooked that information

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

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

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

$$m=\frac{F}{g} = \frac{3011}{9.81}$$ = 306.918
=$$\underline{307kg}$$