Wheel has radius of 300 m how far path length does point on...

A wheel has radius of 3.00 m How far (path length) does point on the circumference travel if the wheel is rotated through the following angles_ respectively? 37.09 (b) 37.0 rad 37.0 rev The tires on new compact car have diameter of 2.0 ft and are warranted for 56,000 miles . Determine the angle (in radians) through which one of these tires will rotate during the warranty period_ rad How many revolutions of the tire are equivalent to your answer in (3)? potter'$ wheel moves uniformly from rest to an angular speed of 0.24 rev/s in 32.0 (a) Find its angular acceleration in radians per second per second_ rad/s? (b) Would doubling the angular acceleration during the given period have doubled final angular speed? Yes

Transcript

0:00 All right, hello.

00:01 In this question we're told we have a radius of three meters on a wheel and we're asked for the path lengths on the point on the circumference if the wheel rotates through three angles, 37 degrees, 37 radians, and 37 revolutions.

00:11 So for all of these we're going to get that our linear distance traveled, d, is going to be our change in theta, our angle, times our radius.

00:20 And our change in angle here has to be in radians.

00:25 That's the way that this is going to work out.

00:27 So we need to convert the angles that are not radians into radians.

00:31 I know that in one full circle there is 180 degrees, or half circle there's 180 degrees, and that's going to have pi radians.

00:38 And then i know that in one revolution, that's one full time around a circle, i have two pi radians.

00:45 So i'm going to have 74 pi radians for this third angle and 37 pi over 180 radians for my first angle.

00:57 So i can get d1, d2, and d3 by just plugging those in.

01:00 And i'll get three values for my distance, 0 .16 meters, 111 meters, and then 697 meters.

01:09 For the second part we're told that new tires have a diameter of two feet, so our radius is one foot, and a warranty for 56 ,000 miles.

01:19 How many rotations will this go through in the warranty period in radians and then in revolutions? so now we're looking for delta theta.

01:26 We know what our linear distance d is.

01:29 It's going to be 56 ,000 miles.

01:32 And so we can use this equation here, and if we solve for delta theta, we're going to get it's going to be d over r...

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