1. (a) An old phonograph record rotates clockwise at 33? rpm...

1. (a) An old phonograph record rotates clockwise at 33? rpm (revolutions per minute). What is its angular velocity in rad/s? (b) If a CD rotates at 22.0 rad/s, what is its angular speed in rpm? 2. Find the period of a record that is rotating at 45 rpm. 3. If the angular velocity of the pulley below is -8.4 rad/s at a given time, and its angular acceleration is -2.8 rad/s2 , what is the angular velocity of the pulley 1.5 s later? 4. Find the angular speed a CD must have to give a linear speed of 1.25 m/s when the laser beam shines on the disk 2.50 cm from its center.

Transcript

00:01 So here in the first part of the question, in this a part, we can say that we are given a record which rotates in the clockwise, it is rotating clockwise that is at the angle of 33 and 1 divided by 3 revolutions per minute.

00:24 So we have to find out the angular velocity in its angular velocity in radian per second.

00:38 So from here, we can say that we know that the angular velocity is given by the formula that is omega which is equals to 2 pi f, where f is the frequency of rotation in this case.

00:52 So we are given the value of the frequency is given that is equals to 33 and 1 divided by 3 revolutions per minute, which means that the record rotate this times 33 and 1 divided by 3 times in a minute.

01:09 So to convert this to radians per second, we need to multiply it with 2 pi divided by 60.

01:19 So 33, 1 divided by 3 multiplied by the 2 pi divided by the 60.

01:25 Now this from here will become in the radian per second, because there are 60 seconds in a minute and 2 pi radian in a 2 pi radian in a circle.

01:37 So this from here will be in radian per second.

01:41 So the frequency in radian per second from here will become equals to 3 .49 radian per second.

01:50 So this is the answer to the part a of the question.

01:54 Now we have to convert it from radian per second to revolution per second.

02:04 So we need to use a formula that is f is equals to omega divided by 2 pi.

02:10 So we are having the value of omega that is equals to 22 radian per second.

02:16 So f from here will become equals to 22 radian per second that is divided by the 2 pi.

02:25 Solving this value from here, we get the value of f that is equals to 3 .50 revolution per minute.

02:31 Hence, this is the answer to the part b for the answer 1.

02:35 For the question 2, we can say that the period of rotation is the time it takes to complete one revolution...

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