Chapter 12: Rotation of a Rigid Body

A solid sphere of radius R is placed at a height of 30 cm on a ${15}^{°}$slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius be released on the same slope in order to equal the sphere's speed at the bottom?

Evaluate the cross products $\overrightarrow{A}\times \overrightarrow{B}$and $\overrightarrow{C}\times \overrightarrow{D}$

Evaluate the cross products$\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{C}\times \overrightarrow{D}$. (part )

Vector $\overrightarrow{A}=3\hat{ı}+\hat{ȷ}$ and vector $\overrightarrow{B}=3\hat{ı}-2\hat{ȷ}+2\hat{k}$ . What is the cross product $\overrightarrow{A}\times \overrightarrow{B}$ ?

An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60rpm to 90 rpm in 10s .

a. What is the tangential acceleration of the pedal?

b. What length of chain passes over the top of the sprocket during this interval?

Force $\overrightarrow{F}=-10\widehat{ȷ}\mathrm{N}$is exerted on a particle at $\overrightarrow{r}=(5\widehat{ı}+5\widehat{ȷ})\mathrm{m}$. What is the torque on the particle about the origin?

A $1.3$kg ball on the end of a lightweight rod is located at $(x,y)=(0.3m,2.0m)$where the $y$axis is vertical. The other end of the rod is attached to a pivot at $(x,y)=(0m,3.0m)$. What is the torque about the pivot? Write your answer using unit vectors.

What are the magnitude and direction of the angular momentum relative to the origin of the particle

What is the angular momentum vector of the diameter rotating disk?

What is the angular momentum vector of the rotating bar in