Problem 35P

What is the distance from the Earth’s center to a point outside the Earth where the gravitational acceleration due to the Earth is of its value at the Earth’s surface?

Solution 35P When the torque is applied on an object that rotating about field axis then that object will undergo angular acceleration.the angular acceleration is quantitative expression of the change in angular velocity that a spinning object undergoes per unit area. The angular acceleration in terms of torque is defined as torque=(moment of inertia)*(angular acceleration) = I = /I The moment of inertia about an axis passing through center of axis is I = mr /2 Where r is radius of disk. To solve this problem we have to knowing some concepts like torque,moment of inertia,rotational dynamics and rotational kinematics. Given data: Mass of the plastic disk m = 200 g = 0.2 kg Radius of disk is r = d/2 = 20/2 = 10 cm = 0.1 m The moment of inertia of the disk is given by I = mr /2 2 I = (0.2 kg)(0.1 m) /2 I = 0.001 kg/m 2 Initial angular speed w = 0i 2 w r 1800 rpm = 1800(2)/(60 rad/s) = 60 rad/s Then the angular acceleration is given by w = w +(t t) r i f i = (w rw)/(tit)f i = (60 rad/s0 rad/s)/(4.0 s) 2 = 15 rad/s Then the net torque applied by motor is = I = (0.001 kg/m )(15 rad/s ) 2 = 0.04686 N/m~0.047 N/m