# physics problem?

Suppose you’re eating in a restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 47.3 cm. You can’t stop thinking about physics even though you’re out with your friends, and decide to calculate the mass of the rotating surface and all the food. If the surface is initially at rest and you exert a tangential force of 2.2 N on it, you observe that the food rotates at a speed of 1.1 rev/s after applying the force consistenty for 1.3 seconds. Find the mass of the disk wtih the food, in kg.

### 1 Answer

- billrussell42Lv 72 weeks agoBest Answer
L = 47.3 cm = 0.473 m

τ = 2.2 N x 0.473 m = 1.0406 Nm

α = τ/I = 1.0406 / I

1.1 rev/s x 2π rad/rev = 6.91 rad/s

ω = ω₀ + αt

ω = 0 + (1.0406 / I)(1.3) = 6.91

I = (1.0406)(1.3) / (6.91) = 0.1957 kg•m²

I = ½MR²

M = 2I/R² = 2(0.1957) / (0.473)² = 1.75 kg

ω = ω₀ + αt

ω is angular velocity in radians/sec

1 radian/sec = 9.55 rev/min

angular acceleration in rad/s²

α = τ/I for constant α

I = moment of inertia in kg•m²

τ = torque in N•m

I is moment of inertia in kg•m²

I = cMR²

M is mass (kg), R is radius (meters)

c = 1 for a ring or hollow cylinder

c = 2/5 solid sphere around a diameter

c = 7/5 solid sphere around a tangent

c = ⅔ hollow sphere around a diameter

c = ½ solid cylinder or disk around its center