Physics, 21.09.2019 08:30 hunterbetterton1

An old-fashioned single-play vinyl record rotates on a turntable at 45.0 rpm. what are (a) the angular velocity in rad/s and (b) the period of the motion?

Answers: 1

Show answers

Answers

The vinyl record, which rotates at 45 rpm, has an angular velocity of 4.71 radians per second, and has a period 1.33 seconds.

Further explanation

Movement is the change of position of an object or a point, movement can be slipt into 2 basic motions, translation and rotation. In the case of our problem, we have pure rotation, since the vinyl record doesn't move anywhere, it sits still while the disc rotates over an axis.

In the problem, we are asked to compute the angular velocity of the vinyl record. We know that the vinyl record makes 45 revolutions per minute, this already is a measure of the angular velocity, however it is a custom to express it in radians per second. Therefor to answer the question we need to change its dimensions, we know that 1 revolution is equal to $2 \pi$ radians, and 1 minute is equal to 60 seconds, therefor:

$45 \frac{rev}{min} = 45 \cdot \frac{2 \pi}{60} \frac{rad}{s} = 4.71 \frac{rad}{s}$

Now let's compute the period. The period is a measure of how much time does a rotating object complete a revolution, and it's computed through the following formula:

$T= \frac{2 \pi}{w}$

Where is the angular velocity. By plugging values we obtain that the period is equal to 1.33 seconds.

Learn morePeriod of other objects: Kinematics of angular movement: Period of data: Keywords

Angular velocity, rotation, period of motion

Answer from: macnasiahamiel

(a)The angular velocity of the single-play vinyl record is $\boxed{\frac{{3\pi }}{2}\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}}$ or $\boxed{4.71\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}}$ .

(b)The time period of rotation of the vinyl record is $\boxed{\frac{4}{3}\,{\text{s}}}$ or $\boxed{1.333\,{\text{s}}}$ .

Further Explanation:

Part (a):

The rpm is the measurement of the number of rotations made by the body in one minute. The angular velocity of a body in the unit of radian per second is the measure of the angle covered by the body in one second.

The angular velocity of the body in radian per second is given by:

$\omega = \left( {rpm} \right) \times \left( {\frac{{2\pi }}{{60}}} \right){{rad} \mathord{\left/ {\vphantom {{rad} {\sec }}} \right.\kern-\nulldelimiterspace} {\sec }}$

Substitute the value of rpm in the above expression.

$\begin{aligned}\omega&= \left( {45\,{{{\text{rev}}} \mathord{\left/ {\vphantom {{{\text{rev}}} {{\text{min}}}}} \right.\kern-\nulldelimiterspace} {{\text{min}}}}} \right) \times \left( {\dfrac{{2\pi }}{{60}}} \right){{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}\\&=\dfrac{3\pi}{2}\,\text{rad/s}\\&\approx4.71\,\text{rad/s}\end{aligned}$

Thus, the angular speed of rotation of the vinyl record in radian per second is $\boxed{\frac{{3\pi }}{2}\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}}$ or $\boxed{4.71\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}}$ .

Part (b):

The time period of rotation of a body is the time taken by the body in completing one revolution. The time period of rotation of the vinyl record is given by:

$T = \dfrac{{2\pi }}{\omega }$ …… (I)

Substitute $\dfrac{{3\pi }}{2}\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}$ for $\omega$ in above expression.

$\begin{aligned}T&= \dfrac{{2\pi }}{{\left( {\dfrac{{3\pi }}{2}} \right)}}\,{\text{s}} \\&={\text{}}\dfrac{4}{3}\,{\text{s}} \\&={\text{ 1}}{\text{.333}}\,{\text{s}} \\\end{aligned}$

Thus, the time period of the vinyl record is $\boxed{\frac{4}{3}\,{\text{s}}}$ or $\boxed{1.333\,{\text{s}}}$ .

Learn More:

A 30.0-kg box is being pulled across a carpeted floor by a horizontal force of 230 n What type of mirror do dentist use Forces of attraction limit the motion of particles most in

Answer Details:

Grade: College

Chapter: Circular motion

Subject: Physics

Keywords: Old fashioned, single play vinyl record, rotates, angular velocity, time period of rotation, revolution per minute, rpm, radian per second.

Answer from: Quest

54 degrees incident angle = reflected angle

angle is from normal turned to line of ray

Answer from: Quest

can somebody give me the answer so i can graduate

Another question on Physics

Physics, 21.06.2019 18:00

Ineed extreme for task 2. my student number is 571721. many to whoever solves this correctly, im in debt to you.

Answers: 2

Answer

Physics, 22.06.2019 09:10

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island

Answers: 2

Answer

Physics, 22.06.2019 10:00

Which fact supports the conclusion that there will be fewer farm managers in the future? a) a farmer manager’s duties vary by the type of farm. b) farm technology is replacing some administrative jobs c) farm managers often need experience but not education. d) administrative duties include budgeting and training staff.

Answers: 2

Answer

Physics, 22.06.2019 10:50

If jerome is swinging on a rope and transferring energy from gravitational potential energy to kinetic energy, is being done.

Answers: 3

Answer

You know the right answer?

An old-fashioned single-play vinyl record rotates on a turntable at 45.0 rpm. what are (a) the angul...

Questions