# Angular acceleration of an arm

## 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.

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.

Is there any diagram associated with your questions which may contain useful information? This question is not solvable without the length of arm.

if you arent solving for torque, why is the length of the arm necessary?

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.

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.

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.

so i substitute the equation for α in v=rω?

what would r be?

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?

wouldn't it be 31?

or .o31 m?

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.

oh dang my bad it was .31!

Now you get it. so now ill just plug in the acceleration i found and the mass

but which mass would i use?

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?

the mass of the arm? correct

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.

How can you get the moment of inertia if you dont have the radius of the ball? 2/5mr^2

i guess, I = ∫ r2d(m) could work

Last edited:
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.