Answer:
frictional force = 0.52 N
Explanation:
diameter of turn table (D1) = 30 cm = 0.3 m
mass of turn table (M1) = 1.2 kg
diameter of shaft (D2) = 1.2 cm = 0.012 m
mass of shaft (M2) = 450 g = 0.45 kg
time (t) = 15 seconds
acceleration due to gravity (g) = 9.8 m/s^{2}
radius of turn table (R1) = 0.3 / 2 = 0.15 m
radius of shaft (R2) = 0.012 / 2 = 0.006 m
total moment of inertia (I) = moment of inertia of turn table + moment of inertia of shaft
I = 0.5(M1)(R1)^{2} + O.5 (M2)(R2)^{2}
I = 0.5(1.2)(0.15)^{2} + O.5 (0.45)(0.006)^{2}
I = 0.0135 + 0.0000081 = 0.0135081
ω₁ = 33 rpm = 33 x \frac{2π}{60} = 3.5 rad/s
α = -ω₁/t = -3.5 / 15 = -0.23 rad/s^{2}
torque = I x α
torque = 0.0135081 x (-0.23) = - 0.00311 N.m
torque = frictional force x R2
- 0.00311 = frictional force x 0.006
frictional force = 0.52 N
