8.4 Velocity and acceleration of a sliding/rolling sphere (Section 9.8). The figure to the right ...
8.4 Velocity and acceleration of a sliding/rolling sphere (Section 9.8). The figure to the right shows a sphere B of radius R moving on a horizontal plane N. B's angular velocity in N and the velocity of Bo (B's geometric center) in N are expressed in terms of time-dependent variables wg, Wy, wz, Vr, vy as nz (a) Denoting Bw as the point of B in contact with N , find BN's velocity and acceleration in N Result: (8.3) (8.4) ny n, Is Nv Is NaB the time-derivative in N of NvBy ? Yes/No (1 the time-derivative in N of FBx /No? Yes/No (c) Now assume B rolls on N (there is sufficient friction between N and B for rolling). Use the definition of rolling to determine another expression for yh and then use it to express v, and vy in terms of R, wzs wy, w'. Also find By's acceleration in N and express it without vz, g, yy by Result: NVBw- (rolling) solve for Ug, y
8.4 Velocity and acceleration of a sliding/rolling sphere (Section 9.8). The figure to the right shows a sphere B of radius R moving on a horizontal plane N. B's angular velocity in N and the velocity of Bo (B's geometric center) in N are expressed in terms of time-dependent variables wg, Wy, wz, Vr, vy as nz (a) Denoting Bw as the point of B in contact with N , find BN's velocity and acceleration in N Result: (8.3) (8.4) ny n, Is Nv Is NaB the time-derivative in N of NvBy ? Yes/No (1 the time-derivative in N of FBx /No? Yes/No (c) Now assume B rolls on N (there is sufficient friction between N and B for rolling). Use the definition of rolling to determine another expression for yh and then use it to express v, and vy in terms of R, wzs wy, w'. Also find By's acceleration in N and express it without vz, g, yy by Result: NVBw- (rolling) solve for Ug, y