1)The blades of a fan running at low speed turn at 260 rpm. When the fan is swit

Question

1)The blades of a fan running at low speed turn at 260 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 300 rpm in 5.60 s. What is the magnitude of the angular acceleration of the blades?

2)A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.30 × 104 rad/s to an angular speed of 3.14 × 104 rad/s. In the process, the bit turns through 1.94 × 104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 7.85 × 104 rad/s, starting from rest?

3)A 3.00 kg puppet oscillates at the end of a light spring of constant k = 2.00 N/m. What is the frequency of the oscillations?

4)It takes a force of 80.0 N to compress the spring of a toy popgun 0.15 m to "load" a 0.15 kg ball. With what speed will the ball leave the gun?

5)A spring that has a force constant of 1000 N/m is mounted vertically on the ground. A block of mass 1.00 kg is dropped from rest from height of 1.50 m above the free end of the spring. By what distance does the spring compress?

6)A 1.55 kg box rests on a plank that is inclined at an angle of 69.0° above the horizontal. The upper end of the box is attached to a spring with a force constant of 25.0 N/m, as shown in the figure. If the coefficient of static friction between the box and the plank is 0.23, what is the maximum amount the spring can be stretched and the box remain at rest?

Explanation / Answer

here,

initial angular speed , Wi = 260 rpm

Wi = 260 * 2pi/60 rad /s

Wi = 27.22 rad/s

final angular speed , Wf = 300 rpm

Wf = 300 * 2 * pi/60

Wf = 31.41 rad/s

time taken ,t = 5.6s

let the angular accelration be a

using first equation of motion

Wf = Wi + a * t

31.41 = 27.22 + 5.6 *a

a = 0.74 rad/s^2

the angular accelration is 0.74 rad/s

please post seperate questions in diffreent post

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