Archive for the ‘Angular and Linear Velocities’ Category

Problem 595

Find the 5th term of the sequence in which t1 = 8 and tn = -3tn-1.

 

 Solution:-

 

t1 = 8

t2 = -3(t1) = -3(8) =-24

r = -3

a5 =  8*(-3)^{4}

a5 = 648

 

Problem 590

Find S10 for the series 2 + 7 + 12 + 17 +…

 

Solution:-

 

a1 = 2, d = 5

S10 = \frac{n}{2}[2*a1 + (n-1)*d]

S10 = \frac{10}{2} [2*2 + (10-1)*5]

S10 = 245

Problem 587

If a wheel with a diameter of 10 feet spins at a rate of 5 revolutions per minute, find the approximate linear velocity in miles per hour. Use \pi = 3.14   .

 

Solution:-

 

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

1.8 miles per hour

Problem 586

If a wheel with a diameter of 30 inches spins at a rate of 40 revolutions per minute, find the approximate linear velocity in miles per hour. Use \pi = 3.14

 

Solution:-

 

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

3.6 miles per hour

Problem 585

If a wheel with a radius of 80 inches spins at a rate of 100 revolutions per minute, find the approximate linear velocity in miles per hour. Use \pi = 3.14  .

 

Solution:-

 

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

48 miles per hour

Problem 584

If a wheel with a radius of 50 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour. Use \pi = 3.14

 

Solution:-

 

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

179 miles per hour

Problem 583

 

Determine the linear velocity of an object with an angular velocity of 10.2 radians per second at a distance of 20 centimeters from the center. Use  \pi = 3.14  . Round the answer to the nearest tenth.

 

Solution:-

Determine the linear velocity using the formula : v = r\omega

 

204.0 centimeters per second

Problem 582

 

Determine the linear velocity of an object with an angular velocity of 5.5 radians per second at a distance of 12 centimeters from the center. Use \pi = 3.14  . Round the answer to the nearest tenth.

 

Solution:-

 

Determine the linear velocity using the formula : v = r\omega

66.0 centimeters per second

Problem 581

Determine the linear velocity of an object with an angular velocity of 3.1 radians per second at a distance of 10 centimeters from the center. Use \pi = 3.14 . Round the answer to the nearest tenth.

 

Solution:-

 

Determine the linear velocity using the formula : v = r\omega

31.0 centimeters per second

Problem  580

 

Determine how long it will take an object to rotate through 4.8 revolutions at an angular velocity of 2.8 radians per second. Use  . Round the answer to the nearest tenth.

 

Solution:-

Determine the angular velocity using the formula: \omega =\frac{\theta }{t}.

10.8 seconds