Question

A heavy turntable, used for rotating large objects, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 0.876 rad/s2.
(a)
What is the moment of inertia of the wheel (in kg · m2)?

_____ kg · m2

(b)What is the mass (in kg) of the wheel?

_________ kg

(c)The wheel starts from rest and the tangential force remains constant over a time period of 6.00 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?

________ rad/s

Answer 1

Answer:

a) $I = 113.014\,kg\cdot m^{2}$, b) $m = 2075.556\,kg$

Explanation:

a) The turntable has the following physical model by using Newton's laws:

$F \cdot R = I \cdot \alpha$

The moment of inertia is:

$I = \frac{F\cdot R}{\alpha}$

$I = \frac{(300\,N)\cdot(0.33\,m)}{0.876\,\frac{rad}{s^{2}} }$

$I = 113.014\,kg\cdot m^{2}$

b) The moment of inertia for a solid cylinder:

$I = \frac{1}{2}\cdot m \cdot R^{2}$

The mass of the turntable is:

$m = \frac{2 \cdot I}{R^{2}}$

$m = \frac{(2)\cdot (113.014\,kg\cdot m^{2})}{(0.33\,m)^{2}}$

$m = 2075.556\,kg$