How to determine the torque of a rotating disc?

[MechaMZ]

how to determine the torque of a rotating disc in order to find the power of motor?

there is a rotating disc, and a ball will pass through and launched by the rotating disc.
the initial speed is 20m/s, and i could determine the rpm from here.

the information i have now:
the disc diameter is 15cm, and the ball diameter is 0.143m and 0.18kg

thank you

 

[tiny-tim]

Hi MechaMZ!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

 

[MechaMZ]

i think to find out the power required by the motor, torque should be found before that.
but what should i do to find out the torque due to these limited information =(

i tried to find out the moment of inertia, so i could determine the torque..
and actually there is another roller under the ball, so i assume the vertical forces are balanced.

where
I =K.M.R²
M is the mass
R is the radius of the object from the center of mass (in some cases, the length of the object is used instead.)
k is a dimensionless constant called the inertia constant that varies with the object in consideration.

Inertial constants are used to account for the differences in the placement of the mass from the center of rotation. Examples include:

* k = 1, thin ring or thin-walled cylinder around its center,
* k = 2/5, solid sphere around its center
* k = 1/2, solid cylinder or disk around its center.

but the mass is referring to the mass of ball or the roller?

and followed by the formula,

torque= I.α
where α is angular acceleration

but what is the time referring to?

 

[tiny-tim]

i tried to find out the moment of inertia, so i could determine the torque..
and actually there is another roller under the ball, so i assume the vertical forces are balanced.
…
but the mass is referring to the mass of ball or the roller?

The mass is the mass of whatever you are working out the moment of inertia of.

but what is the time referring to?

What time?

Sorry, but you seem to be using words somewhat at random …

even with the diagram, I haven't worked out what this problem is about …

is there a disc or a wheel? what is the "roller"? what is the ball "passing through"? how is it launched? is its diameter really 14.3cm?

Can you please write out the whole question for us?

 

[MechaMZ]

hi tim, actually my problem is quite similar with this
https://www.physicsforums.com/showthread.php?t=76293

but i don't know why the mass(or anything else that related to) of the wheel(rubber) is not considered, as we calculating the torque in order to find the motor power..

thank you =)

 

[MechaMZ]

this is what i did..

E= $$\tau \vartheta$$
mgh + 0.5mv² = $$2\tau(\pi/2)$$
since there are 2 motors
(0.18 x 9.81 x 1.2) + (0.5 x 0.18 x 20²) = $$\tau \pi$$
$$\tau = 12.13Nm$$
height of the ball is 1.2m, and the mass is 0.18kg, the initial velocity is 20m/s

but is this the way to calculate the power required for the motor?
there are 2 rotating wheels with 0.15m in diameter.

at linear velocity 20m/s, rpm = 2546.415rpm
power(kW) = $$\tau$$ x 2$$\pi$$ x N / 60000
= 3.23Kw

the answer seems like not correct though =(

 

[nvn]

MechaMZ: Why do you say the ball has a height of 1.2 m? In your diagram, the ball seems to have an initial and final height of 0 m. Secondly, are you sure the ball has an initial velocity of 20 m/s? Did you mean to say the ball has a final (launch) velocity of 20 m/s, when it exits the rotating disks? Are you saying the initial velocity of the ball entering the disks is v1 = (2*g*h)^0.5 = 4.8514 m/s?