Angular acceleration of an arm

  • #1
tristanmagnum
44
0

Homework Statement



Assume that a 1.20-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, the figure. The ball is accelerated uniformly from rest to 9.5m/s in 0.38s , at which point it is released. Assume that the forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at its end.

Part A: Calculate the angular acceleration of the arm.

Part B:Calculate the force required of the triceps muscle.

Homework Equations


i believe angular acceleration=Δω/Δt


The Attempt at a Solution



really lost on this problem physic is not my strong suit.
 

Answers and Replies

  • #2
Periapsis
26
0
Well, for part A, you pretty much solved it already. Just plug in the 9.5m/s for Δω, and .38s for Δt. For part B, remember that F=ma. You calculuated the angular acceleration, and you are given mass, once again, just plug it all in.
 
  • #3
imiuru
44
1
Is there any diagram associated with your questions which may contain useful information? This question is not solvable without the length of arm.
 
  • #4
Periapsis
26
0
if you arent solving for torque, why is the length of the arm necessary?
 
  • #6
imiuru
44
1
Well, for part A, you pretty much solved it already. Just plug in the 9.5m/s for Δω, and .38s for Δt. For part B, remember that F=ma. You calculuated the angular acceleration, and you are given mass, once again, just plug it all in.

The unit for Δω is rad/s. 9.5m/s should be speed.
 
  • #7
imiuru
44
1
if you arent solving for torque, why is the length of the arm necessary?

Torque never come to my mind when i mention the length of the arm.

since v=rω, it is important to have r in order to solve for ω.
 
  • #8
imiuru
44
1
For part A, you can start from the equation "angular acceleration=Δω/Δt". (Note the word angular, acceleration is different from angular acceleration)

By using v=rω, substitute into α =Δω/Δt and you will get the answer.

For part b, it is already answered by Periapsis, except that you should use acceleration instead of angular acceleration in your "F=ma".
 
  • #9
tristanmagnum
44
0
so i substitute the equation for α in v=rω?
 
  • #10
tristanmagnum
44
0
what would r be?
 
  • #11
imiuru
44
1
Originally, you have α=Δω/Δt. Now use ω=v/r to replace the ω in your original equation.

r will be the length of arm. What do you think is the length of arm, according to the diagram provided?
 
  • #12
tristanmagnum
44
0
wouldn't it be 31?
 
  • #13
tristanmagnum
44
0
or .o31 m?
 
  • #14
imiuru
44
1
it's neither of them. Since this has to do with unit conversion, I suggest you revise it from your textbook. You will find yourself solving problems with ease once you have strong command of the basics.
 
  • #15
tristanmagnum
44
0
oh dang my bad it was .31!
 
  • #16
imiuru
44
1
Now you get it.:smile:
 
  • #17
tristanmagnum
44
0
so now ill just plug in the acceleration i found and the mass
 
  • #18
tristanmagnum
44
0
but which mass would i use?
 
  • #19
imiuru
44
1
F=ma says that an object with mass m will experience acceleration a under force F.

The acceleration you obtained belong to which object? Arm? Ball?

Which mass should you use then?
 
  • #20
tristanmagnum
44
0
the mass of the arm? correct
 
  • #21
Periapsis
26
0
add the two masses up.
 
  • #22
imiuru
44
1
Ops! Part B appeared to be more tricky than I initially thought. You can forget using F=ma to solve it.

May I know where you get this problem?

There are a few assumptions to be made in order to solve this problem. Still, it takes plenty of steps to get the final answer.

First, you must draw the free body diagram with the arm and the ball as the system. This will help you to picture how each components contribute to the τ (net torque) of the system.

With τ=Iα,where I is the moment of inertia, α is the angular acceleration, you will be able to get the value of τ, provided you know how to calculate I. (refer to your textbook on moment of inertia for uniform rod)

τ(tricep) - τ(arm) - τ(ball) = τ(net)

Using the above equation, you will be able to solve for τ(tricep) and in turn, F(tricep).

You will need this in your workout: τ=Fr where r is the distance from the pivot point to the point where force is applied.
 
  • #23
Periapsis
26
0
How can you get the moment of inertia if you dont have the radius of the ball? 2/5mr^2
 
  • #24
Periapsis
26
0
i guess, I = ∫ r2d(m) could work
 
Last edited:
  • #25
imiuru
44
1
Maybe there is no need to calculate moment of inertia. Use τ=Fr to calculate τ(net) will do. F can be obtained through F=ma and r can be obtained through finding the centre of mass of the system.

Anyways, it is up to the original question raiser to do the math.
 
  • #26
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
38,454
7,965
How can you get the moment of inertia if you dont have the radius of the ball? 2/5mr^2
You can treat the ball as a point mass, making its MI about the arm's axis easy. The Mi of the arm is obtained by treating it as a rod rotated about one end.
 
Last edited:
  • #27
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
38,454
7,965

Homework Statement



Assume that a 1.20-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, the figure. The ball is accelerated uniformly from rest to 9.5m/s in 0.38s , at which point it is released. Assume that the forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at its end.

Part A: Calculate the angular acceleration of the arm.

Part B:Calculate the force required of the triceps muscle.
.
Unless there's more info in the diagram, there's not enough to determine the force from the triceps. All you can do is calculate the torque.
 

Suggested for: Angular acceleration of an arm

Replies
1
Views
299
Replies
17
Views
993
Replies
13
Views
482
  • Last Post
Replies
33
Views
1K
  • Last Post
Replies
2
Views
298
Replies
8
Views
486
  • Last Post
Replies
3
Views
253
Replies
3
Views
639
  • Last Post
Replies
7
Views
375
Replies
23
Views
383
Top