Consider the diagram below. Calculate the value of F2. Calculate the value of the distance X. Consider the diagram below. Calculate the tension, T, in the wire. Calculate the magnitude and direction of the vertical force the wall exerts on the hinge. A solid sphere is attached to the shaft of an electric motor. The sphere's mass is 3.00 kg and its radius is 0.150 meters. The electric motor increases the sphere's rotation from 4.00 revolutions/second to 20.0 revolutions/second in 8.00 seconds. Calculate the sphere's angular acceleration. Calculate the torque applied to the sphere. Calculate the disk's angular displacement during the time its rotation increased from 4.00 revoutions/second to 20.0 revolutions/second. Calculate the work done by the electric motor during the time the sphere's rotation increased from 4.00 revolutions/second to 20.0 revolutions/second.
Explanation / Answer
Given that the mass of sphere is m = 3.00 kg radius is r = 0.150 m Initial angular velcoity is 1 = 4.0 rev/s = 25.13 rad/s final angular velcoity is 2 = 20.0 rev/s = 125.6 rad/s Time taken t = 8.00s ------------------------------------------------------------------ (a) Angular velcoity is = (2 - 1) / t = 12.56 rad/s2 (b) Moment of inertia of the sphere is I = (2/5)mr2 = 0.027 kg.m2 Now the torque is = I = 0.339 N.m (c) Angular distance is = 22 - 12 / 2 = 602.86 rad Now the net displacenent is ' = 95.99 rad (d) The work done is W = (1/2)I22 - (1/2)I12 =204.41 J (b) Moment of inertia of the sphere is I = (2/5)mr2 = 0.027 kg.m2 = 0.027 kg.m2 Now the torque is = I = 0.339 N.m (c) Angular distance is = 22 - 12 / 2 = 602.86 rad Now the net displacenent is ' = 95.99 rad (d) The work done is W = (1/2)I22 - (1/2)I12 =204.41 J =204.41 J