Can someone please help me with this rotational mechanics question please?

s3a

Nov 2008
624
5
The question is: http://i.imgur.com/pB7pm.png

I get (a) 66.1175 rad/s^2 but am stuck right away on (b). It seems to me that (a) and (b) should have the same answer however that is not the case. As for (c) and (d), I haven't been able to get to them yet but it would appreciated if someone could show me their work for (b) => (d).

Thanks in advance!
 
May 2010
20
8
The question is: http://i.imgur.com/pB7pm.png

I get (a) 66.1175 rad/s^2 but am stuck right away on (b). It seems to me that (a) and (b) should have the same answer however that is not the case. As for (c) and (d), I haven't been able to get to them yet but it would appreciated if someone could show me their work for (b) => (d).

Thanks in advance!

\(\displaystyle \tau=r\times F\)

\(\displaystyle \tau=I\alpha\)

Angular acceleration depends on the torque, and the torque depends on the angle between F and r. Therefore angular acceleration depends on the angle between F and r. The moment you release the block, F is perpendicular to r. However as the block falls the angle between F and r becomes more obtuse, making the torque smaller and the angular acceleration smaller.
 

s3a

Nov 2008
624
5
It sounds like I need derivatives and rates of change but this course does not involve calculus...so how would I go about this mathematically?
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
It sounds like I need derivatives and rates of change but this course does not involve calculus...so how would I go about this mathematically?
set up a system of two equations.

let \(\displaystyle m\) = block mass

\(\displaystyle I\) = cylinder's rotational inertia

\(\displaystyle T\) = tension in the string

\(\displaystyle R\) = cylinder radius

\(\displaystyle a\) = linear acceleration of the block

\(\displaystyle \alpha\) = angular acceleration of the cylinder


net force acting on the block ...

\(\displaystyle mg - T = ma\)

net torque acting on the cylinder ...

\(\displaystyle TR = I\alpha\)

the "tie" between the two equations is \(\displaystyle \alpha = \frac{a}{R}\)

solve the system for the linear acceleration of the block and the rest should be rather easy to do.