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

a)
`I = 113.014\,kg\cdot m^(2)`, b)
`m = 2075.556\,kg`

Step-by-step 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 = (F\cdot R)/(\alpha)`

`I = ((300\,N)\cdot(0.33\,m))/(0.876\,(rad)/(s^(2)) )`

`I = 113.014\,kg\cdot m^(2)`

b) The moment of inertia for a solid cylinder:

`I = (1)/(2)\cdot m \cdot R^(2)`

The mass of the turntable is:

`m = (2 \cdot I)/(R^(2))`

`m = ((2)\cdot (113.014\,kg\cdot m^(2)))/((0.33\,m)^(2))`

`m = 2075.556\,kg`