 A 73,000 g Ferris wheel accelerates from rest to an angular speed of 6.2 rad/s in 2 minutes. Considering the wheel as a hollow circular disk of radius 200 cm, calculate the net force on it?

1. Convert mass from grams to kilograms:

m = 73,000 \, \text{g} = 73 \, \text{kg}

2. Convert radius from centimeters to meters:

r = 200 \, \text{cm} = 2 \, \text{m}

3. Convert time from minutes to seconds:

t = 2 \, \text{minutes} = 120 \, \text{seconds}

4. Calculate angular acceleration:

\alpha = \frac{\omega_f - \omega_i}{t} = \frac{6.2 \, \text{rad/s} - 0 \, \text{rad/s}}{120 \, \text{s}} = 0.0517 \, \text{rad/s}^2

5. Moment of inertia of a hollow circular disk:

I = m \cdot r^2 = 73 \, \text{kg} \cdot (2 \, \text{m})^2 = 292 \, \text{kg} \cdot \text{m}^2

6. Calculate net torque:

\tau = I \cdot \alpha = 292 \, \text{kg} \cdot \text{m}^2 \times 0.0517 \, \text{rad/s}^2 = 15.1044 \, \text{N} \cdot \text{m}

7. Calculate net force (since torque = force × radius):

F = \frac{\tau}{r} = \frac{15.1044 \, \text{N} \cdot \text{m}}{2 \, \text{m}} = 7.5522 \, \text{N}

Rounding to a sensible number of significant figures gives the net force:

F\approx7.55\,\text{N}

Therefore, the net force on the Ferris wheel is approximately 7.55\,\text{N} .