Question

The turntable of the record player is turning at 45 rounds per minute. A small object is at rest on the turntable at a distance d = 10 cm from the centre. Its velocity
A: is tangent to the circumference of radius d and has a magnitude of about 0.47 m/s
B: is tangent to the circumference of radius d and has a magnitude of about 47 m/s
C: is tangent to the circumference of radius d and has a magnitude of about 4.7 m/s
D: is directed radially and has a magnitude of about 0.47 m/s
E: is directed radially and has a magnitude of about 47 m/s

Answer 1

Answer on Question 77750, Physics, Mechanics, Relativity

Question:

The turntable of the record player is turning at 45 rounds per minute. A small object is at rest on the turntable at a distance $d = 10 \, \text{cm}$ from the centre. Its velocity

A) is tangent to the circumference of radius $d$ and has a magnitude of about $0.47 \, \text{m/s}$

B) is tangent to the circumference of radius $d$ and has a magnitude of about $47 \, \text{m/s}$

C) is tangent to the circumference of radius $d$ and has a magnitude of about $4.7 \, \text{m/s}$

D) is directed radially and has a magnitude of about $0.47 \, \text{m/s}$

E) is directed radially and has a magnitude of about $47 \, \text{m/s}$

Solution:

Let's first convert rounds per minute to radians per second:

$$\omega = \frac{45 \text{ rounds}}{1 \text{ min}} \cdot \frac{1 \text{ min}}{60 \, \text{s}} \cdot \frac{2\pi \text{ rad}}{1 \text{ round}} = 4.7 \, \frac{\text{rad}}{\text{s}}.$$

We can find the velocity of the object from the formula:

$$v = d\omega,$$

here, $\omega$ is the angular velocity of the turntable, $d$ is the distance from the center to the object.

Then, we get:

$$v = d\omega = 0.1 \, \text{m} \cdot 4.7 \, \frac{\text{rad}}{\text{s}} = 0.47 \, \frac{\text{m}}{\text{s}}.$$

The velocity of the object is tangent to the circumference of radius $d$.

Answer:

A) is tangent to the circumference of radius $d$ and has a magnitude of about $0.47 \, \text{m/s}$

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