Posted by **Oisin** on Tuesday, July 20, 2010 at 8:53am.

A constant force of 20N is applied tangentially to a string wound on the rim of a 40 cm diameter wheel, initially at rest.

(i) How much work does this force do as it turns the wheel through 45„a?

(3 %)

(ii) If the wheel has mass 8.0 kg and radius of gyration 15 cm, how long does it take the wheel to rotate through this angle?

- physics -
**drwls**, Tuesday, July 20, 2010 at 10:07am
(i) 20N * 0.2 m * (angle in radians).

I cannot interpret your angle symbol, which shows up here as ,,a.

(ii) Angular acceleration rate = (Torque)/(Moment of inertia)

= (Torque)/[(Mass)*Rg^2]

The torque is 4 N*m

Angular acceleration =

4 N*m/(8*.15^2 kg m^2) = 22.2 rad/s^2

Time required to rotate angle theta =

2*(theta)/(angular acceleration rate)

- physics -
**Oisin**, Tuesday, July 20, 2010 at 10:12am
so for the first part 20N * 0.2m * 2pi is that correct?

also how did you get your torque?

(iii) What is the angular momentum of the wheel after this time?

- physics -
**drwls**, Tuesday, July 20, 2010 at 11:07am
You never said the angle turned was 2 pi. You typed 45,,a

Torque is force times lever arm (in this case, wheel radius)

(iii) Angular momentum after time T is

(Torque)*(Time) =

(Moment of inertia)*(angular velocity)

- physics -
**Oisin**, Tuesday, July 20, 2010 at 11:17am
no i mean to convert 45degrees into rads you multiply by 2pi

thanks for your help

- physics -
**drwls**, Tuesday, July 20, 2010 at 12:04pm
45 degrees is pi/4 radians. You multiply by pi/180 radians per degree, NOT 2 pi

- physics -
**Oisin**, Tuesday, July 20, 2010 at 4:40pm
how did u find the angular velocity?

im tryin to use v = wr but i don't know where to find the normal velocity of the rim

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