Question

A bicycle wheel is rotating at 40rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.46rad/s2 .

How many revolutions does the wheel make during this time?

also,

A high-speed drill rotating ccw at 2100rpm comes to a halt in 3.00s .

What is the drill's angular acceleration?

How many revolutions does it make as it stops?

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last

A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 mabove the ground traveling at an angle of 30 ? above the horizontal. Top-rated javelin throwers do throw at about a 30 ? angle, not the 45 ? you might have expected, because the biomechanics of the arm allow them to throw the javelin much faster at 30 ? than they would be able to at 45 ? . In this throw, the javelin hits the ground 52m away.

What was the acceleration of the javelin during the throw? Assume that it has a constant acceleration.

Answer 1

Part A)

40 rpm converts to 4.19 rad/s

The acceleration is .46 rad/s²

You will apply the following formula...

Then divide by 2pi to convert to revolutions. Since you did not type in the time, I can't go any further but you can. If you need me to help with it, comment below...

Part B)

First 2100 rpm converts to 219.9 rad/s

For the acceleration, apply wf = wo + at

0 = 219.9 + a(3)

a = -73.3 rad/s² (Negative since it is slowing down)

For the revolutions, apply the equation from part A and get...

Theta = 329.85 rad

Divide by 2pi and get 52.5 revs

Part C)

In the x direction, the velocity is found from d = v_xt and v_x = vcos30 = .866v

52 = .866vt

t = 60/v

In the y direction...

d = vot + .5at²

-2 = vsin(30)(t) + .5(-9.8)(t²)

-2 = .5vt - 4.9t²

Sub in t from above

-2 = .5(60/v) - 4.9(60/v)²

-2 = 30/v - 17640/v²

Multiply everything by v²

-2v² = 30v - 17640

Put in standard form

2v² +30v-17640 = 0

Put in the quadratic equation to get the roots

The roots are...86.7 and -101.7

Since the velocity is not negative, we accept 86.7 for the velocity

Finally apply vf² = vo² + 2ad

86.7² = 0 + 2(a)(.7)

a = 5369.2 m/s²