calculate the linear speed of a point on the record at the beginning and the end of the record that rotates at 33rev/min r1=7cm,r2=15cm
To calculate the linear speed of a point on the record, you need to use the formula:
Linear Speed = Angular Speed × Radius
First, let's calculate the angular speed of the record. The angular speed is given in terms of revolutions per minute (rev/min). To convert it to radians per second (rad/s), we need to remember that one revolution is equal to 2π radians.
Given:
Angular Speed (ω) = 33 rev/min = 33 × 2π rad/min
To convert rad/min to rad/sec, we need to divide by 60 (since 1 minute has 60 seconds):
Angular Speed (ω) = (33 × 2π) / 60 rad/sec
Next, let's calculate the linear speed at the beginning of the record (r1 = 7 cm):
Linear Speed at the beginning (v1) = Angular Speed × Radius1
v1 = (ω) × r1
= [(33 × 2π) / 60] × 7 cm/sec
Now, let's calculate the linear speed at the end of the record (r2 = 15 cm):
Linear Speed at the end (v2) = Angular Speed × Radius2
v2 = (ω) × r2
= [(33 × 2π) / 60] × 15 cm/sec
By plugging in the values and performing the calculation, you can find the linear speed at the beginning and the end of the record.