Rotation cylinder, angular acceleration, picture, need help?

Question

I need help badly !!!

Here's a picture of the figure/question

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c10/fig10_42.gif

In Fig. 10-44, a cylinder having a mass of 3.2 kg can rotate about its central axis through point O. Forces are applied as shown: F1 = 6.2 N, F2 = 3.0 N, F3 = 5.0 N, and F4 = 9.5 N. Also, r = 5.8 cm and R = 16 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)

I need to get a solution rather than just an answer, i need to learn, thanks to everyone who posts.

-Joe

Answer 1

There is an equation similar to "F=ma" that deals with angular motion. But instead of force (F), it uses torque (τ); instead of mass (m), it uses "moment of inertia" (I); and instead of acceleration (a), it uses "angular acceleration" (α).

Torque = (moment of inertia) × (angular acceleration)

τ = Iα

Torque equals (force)×(lever arm). The "lever arm" is the perpendicular separation between the line of force and the axis.

In the diagram, there are four forces, therefore four torques. You need to add them all up to get the total torque (τ)

Torque_1 = F1 × R (positive because it pulls counter-clockwise).
Torque_2 = −F2 × R (negative because it pulls clockwise)
Torque_3 = −F3 × r (negative because it pulls clockwise).
Torque_4 = F4 × 0 (zero because the lever arm is zero).

Add up those four torques to get "τ".

Next, you need to know what the moment of inertia of the cylinder is. From your book, you can find that the moment of inertia of a solid cylinder is:

I = mR²/2

(where "m" is the cylinder's mass).

Now that you have "τ" and "I", you can solve for "α".

Answer 2

Calculate the torque due to each force: Torque is equal to force crossed with radius.

F_1 --> 6.2*16= 99.2 N-cm
F_2 ---> -3 * 16 = -48 N-cm [negative because it is clockwise]
F_3 --> -5 * 5.8 = -29 N-cm
F_4 --> ZERO [it is making an angle of zero with the radius...so there is no torque. This is why you cannot twist a screwdriver by pushing it sideways].

Total torque = 22.2 N-cm = .222 N-m

Angular acceleration is equal to the torque divided by the moment of inertia.

The moment of inertia for a cylinder is 1/2mr^2 = 1/2*3.2*16^2 =409.6 kg-cm^2 = .0409 kg-m^2

So the angular acceleration is .222/.0409 = 5.4 radians per second per second

Answer 3

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