# Rotational motion question

• icg
In summary, a first-time poster on a forum is seeking help with calculating the linear acceleration of a bicycle with a wheel diameter of 0.650 m. Another user provides a solution using angular acceleration and the conversion from rpm to rad/s. Additionally, the second user poses a question about the relationship between linear and angular velocity and acceleration in regards to a car's tires with a diameter of 0.908 m.
icg
Hey everyone, first time poster here It's a really great forum though!

I can't seem to figure out this problem. If anyone could help that would be great.

1.A bicycle has wheels with a diameter of 0.650 m. It accelerates uniformly and the rate of rotation of its wheels increases from 177rpm to 275rpm in a time of 18.5 s. Find the linear acceleration of the bicycle.

I converted rpm to rad/s, and then found angular acceleration using a=vf-vi/t, but how do you find the linear acceleration given the diameter.

And there's also this one:

2.The tires of a car make 78.0 revolutions as the car reduces its speed uniformly from 92.5 km/hr to 55.9 km/hr. The tires have a diameter of 0.908 m. What was the angular acceleration?

If you start with the definition of an angle as the ratio of arc length to radius, you see that the distance the center of a wheel moves when roilling without slipping is proportional to its angular displacement (rotation in radians). It follows that linear velocity is proportional to angular velocity and linear acceleration is probportional to angular acceleration. Can you come up with these relationships?

The radius is half the diameter, isn't it? ;)

## 1. What is rotational motion?

Rotational motion is the movement of an object around a fixed point or axis. It is different from linear motion, which is the movement of an object in a straight line.

## 2. What is the difference between angular velocity and linear velocity?

Angular velocity is the rate at which an object rotates around a fixed point or axis, measured in radians per second. Linear velocity is the rate at which an object moves in a straight line, measured in meters per second.

## 3. How is torque related to rotational motion?

Torque is the force that causes an object to rotate around an axis. The greater the torque applied to an object, the faster it will rotate. This is known as the rotational equivalent of force, as defined by Newton's second law.

## 4. Can rotational motion be measured?

Yes, rotational motion can be measured using various units such as radians, degrees, revolutions, and hertz. It can also be measured using instruments such as a protractor, gyroscope, or tachometer.

## 5. What are some real-life examples of rotational motion?

Examples of rotational motion include the rotation of the Earth around its axis, the spinning of a top, the movement of a bicycle wheel, and the motion of a wind turbine. Many machines also use rotational motion, such as engines, motors, and fans.

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