1) A dentist causes the bit of a high speed drill to accelerate from an angular

Question

1) A dentist causes the bit of a high speed drill to accelerate from an angular speedof 1.05x10 4 rad/s to an angular speed of 3.14x104rad/s. In the process, the bit turns through 1.88x104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 7.85x10 4 rad/s… starting from rest?

3.37 s 7.5 s 0.33 s 0.75 s 73 second

2) A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon string that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 47 rev/s, and its tip has a tangential speed of 54 m/s.

· What is the length of the rotating string?

18m 81 m 0.18 m 0.81 m 5.0 m

3) The planet Mercury is approx. 5.79 x107 km from the sun, If it takes Mercury 88 days to orbit the sun,

· What is the speed of Mercury in meters per second (m/s)?

Explanation / Answer

1) w^2 = w0^2 + 2 alpha theta

(3.14E4)^2 =(1.05E4)^2 + 2*alpha*1.88E4

alpha=23290

w = w0+ alpha t

t = 7.85E4/23290=3.37 s

2)

w = v /r

47*2*pi = 54/r
r=0.18 m

3)

v = 2 pi r/t = 2*pi*5.79E10/(88*24*60*60)=47848 m/s

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