If a hoop, disk and sphere of equal masses and radii where allowed to roll as shown, would they all reach the bottom together?

I sphere < I solid cylndr < I hoop

Easiest

to rotate

Hardest

to rotate

1st

2nd

3rd

Torque is a twisting force. It’s magnitude is r x F.

Where r is the “moment arm” or distance to the axis of rotation.

You can increase torque by just increasing the moment arm.

This is how many tools (levers, wrenches) can twist things easily.

The maximum torque is when r and F are at 90º.

The direction of the torque is along the axis of rotation,

perpendicular to the plane of rotation, as defined by a right hand rule: extend fingers along r from center outward, allow fingers to curl in direction of F applied, and your thumb indicates the direction of the torque.

boy - girl = 0

r x F - r x F = 0

1m x 800N - x x 350N = 0

solve x:

x = 800/350 = 2.16 m

What if all forces are not at right angles wrt the moment arm ?

1. Draw an extended FBD

2. 2. T =0

3. Use T= r x F = r F sin for each torque

First lets solve the case where the man is not there and the boom has a mass of 500 kg .

hinge

boom

Now solve for tension in the cable when a 80 kg man stands 2 meters from the wall.

Θ = 60, μ = 0.5 m= 100 kg

Spinning wheel, CM not translating (Vcm=0)

Spinning wheel, CM translating (Vcm >0) {rolling}

Calculate v at all the points if R = 1m and = 1 rad/sec

Vp’=

Vcm=

Vp=

+1m/s

0

-1m/s

Calculate v at all the points if R = 1m and = 1 rad/sec

Vp’=

Vcm=

Vp=

+2 m/s

+1 m/s

0 m/s

Is this disk rolling or spinning in place?

Angular momentum

L= r x p = r x mv