A 2000kg ferris wheel accelerates from rest to an angular speed of 2.0 rad/s in 12 secs. Approximate the ferris wheel as a circular disk with a radius of 30m. what iss the net torque on the wheel
Torque*time=momentofInertia*final angular speed.
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
To find the net torque on the ferris wheel, we need to use the formula:
Net Torque = Moment of Inertia * Angular Acceleration
First, let's find the moment of inertia of the circular disk. The moment of inertia of a solid disk rotating around its central axis is given by:
Moment of Inertia = (1/2) * mass * radius^2
Given:
Mass of the ferris wheel (m) = 2000 kg
Radius of the ferris wheel (r) = 30 m
Moment of Inertia = (1/2) * 2000 kg * (30 m)^2
Moment of Inertia = 900,000 kg·m^2
Next, we need to calculate the angular acceleration of the ferris wheel. The angular acceleration can be found using the formula:
Angular Acceleration = Change in Angular Velocity / Time
Given:
Angular speed at the end (ωf) = 2.0 rad/s
Time interval (t) = 12 s
Initial angular speed (ωi) = 0 rad/s (as the wheel starts from rest)
Change in Angular Velocity = ωf - ωi
Change in Angular Velocity = 2.0 rad/s - 0 rad/s
Change in Angular Velocity = 2.0 rad/s
Angular Acceleration = (2.0 rad/s) / (12 s)
Angular Acceleration = 0.167 rad/s^2
Now, we can find the net torque:
Net Torque = Moment of Inertia * Angular Acceleration
Net Torque = 900,000 kg·m^2 * 0.167 rad/s^2
Net Torque ≈ 150,300 N·m
Therefore, the net torque on the ferris wheel is approximately 150,300 N·m.
To find the net torque on the ferris wheel, we can use the equation:
net torque = moment of inertia * angular acceleration
First, let's find the moment of inertia of the ferris wheel. Since we are approximating it as a circular disk, we can use the moment of inertia formula for a solid disk:
moment of inertia = (1/2) * mass * radius^2
Given that the mass of the ferris wheel is 2000 kg and the radius is 30 m, we can calculate the moment of inertia:
moment of inertia = (1/2) * 2000 kg * (30 m)^2 = 900,000 kg*m^2
Next, we need to find the angular acceleration. We can use the formula:
angular acceleration = change in angular speed / time
Given that the initial angular speed is 0 rad/s and the final angular speed is 2.0 rad/s, and the time is 12 seconds, we can calculate the angular acceleration:
angular acceleration = (2.0 rad/s - 0 rad/s) / 12 s = 2.0 rad/s / 12 s = 0.1667 rad/s^2
Finally, we can calculate the net torque:
net torque = 900,000 kg*m^2 * 0.1667 rad/s^2 ≈ 150,003 N*m
Therefore, the net torque on the ferris wheel is approximately 150,003 N*m.