Homework Help: Physics

Posted by Una on Sunday, December 18, 2011 at 1:46pm.

I need help with this question please. A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward such that the cylinder is suspended in midair for a brief time interval (change in)t and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is (1/2)mR^2.
What is the linear acceleration of the person's hand during the time interval change in t?

Physics - drwls, Sunday, December 18, 2011 at 3:09pm
Since the cylinder's center of mass is not moving up or down, T = m g
to maintain translational equilibrium

The applied torque is T*R = m*g*R.

That equals the rate of change of angular momentum,
d/dt(I*w) = (mR^2/2)dw/dt = m*g*R

m cancels out and
dw/dt = g/(2R) rad/s^2 = alpha

The linear acceleration of the person's hand is alpha*R = g/2

Cute problem!
Physics - okovko, Monday, December 10, 2012 at 2:46am
Well, the posted solution is incorrect.

Te => tension, To => torque, al => alpha

Te = mg
To = I * al = Te * R
0.5mR^2 * al = mgR
al * R = 2g = a

Answer this Question

Related Questions

Physics - I need help with this question please. A solid cylinder of mass m and ...
physics - A string is wrapped around a uniform solid cylinder of radius r. The ...
physcs - A string is wrapped around a uniform solid cylinder of radius 3.10 cm, ...
Physics - A massless string is wrapped around a cylinder of mass 0.400 kg and ...
Physics - Consider a stainless steel annular disk with an outer radius 66 mm and...
physics - "A solid cylinder and a thin-walled hollow cylinder have the same...
physics - "A solid cylinder and a thin-walled hollow cylinder have the ...
Physics - Consider a stainless steel annular disk with an outer radius 68mm and ...
Physics - Consider a stainless steel annular disk with an outer radius 68mm and ...
Physics - Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, ...

For Further Reading

First Name:
School Subject:
Answer: