Question

If an object moves in uniform circular motion in a circle of radius R = 1.0 meter, and the object takes 4.0 seconds to complete ten revolutions, calculate the magnitude of the velocity around the circle. (Note: Remember, 10 revolutions is a counting number and not a measurement.) v=_____ m/s 1.6 m/s 2.5 m/s 5 m/s 16 m/s

Answer 1

Answer: 2.5 m/s

Explanation: The velocity in in uniform circular motion is given by:

v=w^2*r where w is angular frequency

w=2*Pi/T where T is the period

Finally we can calculate v= (2*Pi)^2/T^2*R where R=1 m

Answer 2

16m/s

Step-by-step explanation:

The velocity v is given by the following relationship;

`v=\omega R.......... (1)`

where
`\omega` is the angular velocity and R is the radius of the circular path. Angular velocity is defined as the number of revolutions made by a body in circular motion per unit time or the angle turned through per unit time. It is measured in radians per second.

Also, the following relationship holds for
`\omega`;

`\omega=\theta /t...............(2)`

where
`\theta` is the angle turned through and t is the time taken.

Given; t = 4s, number of revolutions n = 10.

The angle turned can be obtained from the number of revolutions by recalling the following;

`1 revolution=2\pi rad\\hence\\10revolutions=10*2\pi rad=20\pi rad`

Hence;
`\theta=20\pi rad`

Substituting
`\theta` and t into equation (2), the obtain the angular velocity as follows;

`\omega=20\pi/4\\\omega=5\pi rads^{-1`

Finally we substitute into equation (1) to obtain the linear velocity v as required.

`v=5\pi*1=5\pi m/s`

Taking
`\pi =22/7`;

v = 15.7m/s which is approximately 16m/s