r = 0.04m

1265 rev/min

a.)\(\displaystyle{\left({\frac{{{1265}{r}{e}{v}}}{{\min{u}{t}{e}}}}\right)}{\left({\frac{{{1}\min}}{{{60}{\sec}}}}\right)}{\left({\frac{{{2}\pi{r}{a}{d}}}{{{r}{e}{v}}}}\right)}={132.47}{\frac{{{r}{a}{d}}}{{{\sec}}}}\)

\(\displaystyle\omega={132.47}{r}{a}\frac{{d}}{{\sec{}}}\)

b.) The linear speed is called the tangential velocityalso

\(\displaystyle{V}_{{{\tan}}}={r}\omega\)

\(\displaystyle{V}_{{{\tan}}}={\left({0.022}\right)}{\left({132.47}\right)}\)

\(\displaystyle{V}_{{{\tan}}}={2.914}\frac{{m}}{{s}}\)

c.)\(\displaystyle{a}_{{{c}{e}{n}{t}}}={r}\omega^{{{2}}}\)

\(\displaystyle{a}_{{{c}{e}{n}{t}}}={\left({0.04}\right)}{\left({132.47}\right)}^{{{2}}}\)

\(\displaystyle{a}_{{{c}{e}{n}{t}}}={701.9}\frac{{m}}{{s}^{{{2}}}}\)

d.)\(\displaystyle{V}_{{{\tan}}}={r}\omega\)

\(\displaystyle{V}_{{{\tan}}}={\left({0.04}\right)}{\left({132.47}\right)}\)

\(\displaystyle{V}_{{{\tan}}}={5.299}\frac{{m}}{{s}}\)

D=VT

D= (5.299)(1.96)

D= 10.386 m

1265 rev/min

a.)\(\displaystyle{\left({\frac{{{1265}{r}{e}{v}}}{{\min{u}{t}{e}}}}\right)}{\left({\frac{{{1}\min}}{{{60}{\sec}}}}\right)}{\left({\frac{{{2}\pi{r}{a}{d}}}{{{r}{e}{v}}}}\right)}={132.47}{\frac{{{r}{a}{d}}}{{{\sec}}}}\)

\(\displaystyle\omega={132.47}{r}{a}\frac{{d}}{{\sec{}}}\)

b.) The linear speed is called the tangential velocityalso

\(\displaystyle{V}_{{{\tan}}}={r}\omega\)

\(\displaystyle{V}_{{{\tan}}}={\left({0.022}\right)}{\left({132.47}\right)}\)

\(\displaystyle{V}_{{{\tan}}}={2.914}\frac{{m}}{{s}}\)

c.)\(\displaystyle{a}_{{{c}{e}{n}{t}}}={r}\omega^{{{2}}}\)

\(\displaystyle{a}_{{{c}{e}{n}{t}}}={\left({0.04}\right)}{\left({132.47}\right)}^{{{2}}}\)

\(\displaystyle{a}_{{{c}{e}{n}{t}}}={701.9}\frac{{m}}{{s}^{{{2}}}}\)

d.)\(\displaystyle{V}_{{{\tan}}}={r}\omega\)

\(\displaystyle{V}_{{{\tan}}}={\left({0.04}\right)}{\left({132.47}\right)}\)

\(\displaystyle{V}_{{{\tan}}}={5.299}\frac{{m}}{{s}}\)

D=VT

D= (5.299)(1.96)

D= 10.386 m