15 Questions
What is the characteristic of an object undergoing uniform circular motion?
Constant angular velocity
What is the direction of centripetal force?
Radial towards the center of the circle
What is the unit of angular acceleration?
radians per second squared
What is the relationship between linear speed and angular velocity?
Linear speed is proportional to angular velocity
How many revolutions does an object make in one minute if it completes 9.47 revolutions in 16 seconds?
45.5 revolutions per minute
What is the direction of the centripetal force acting on an object moving in a circular path?
Towards the center of the circle
An object is moving in a circular path with a constant angular acceleration. What can be said about its linear speed?
It is increasing
A car is moving through a levelled curve with a constant speed. What can be said about its angular acceleration?
It is zero
A rotating cylinder completes 10 revolutions in 2 minutes. What is its angular velocity in revolutions per minute?
5 RPM
An object is moving in a vertical circular path. What is the minimum speed required for it to complete the loop?
The speed is dependent on the radius of the loop
What is the direction of the angular velocity vector in the given circular motion?
Parallel to the axis of rotation
What is the linear speed of a point on the circumference of the cylinder?
4.4 m/s
What is the centripetal force required to keep the point on the circumference of the cylinder in circular motion?
Directed radially inward towards the axis of rotation
How many revolutions will the cylinder make in 1 second?
1.59 revolutions
What is the angular acceleration of the cylinder if its angular velocity increases from 10 rad/s to 12 rad/s in 2 seconds?
1 rad/s²
Study Notes
Circular Motion
- The relation 𝒗 = 𝒓𝝎 does not hold for tangential and angular velocity vectors that point in different directions.
Uniform Circular Motion
- The angular velocity is constant in uniform circular motion.
- Apply Newton's laws of motion and energy conservation principles to analyze circular motion in:
- Vertical plane (e.g., motion in a vertical loop of an amusement park ride)
- Horizontal plane (e.g., rotating cylinder, moving through a levelled or banked curve)
Rotating Cylinder
- Example: a cylinder of radius 0.7 m rotating about its axis at 10 rad/s.
Solve a circular motion problem involving velocity and angular velocity vectors. Calculate the velocity of a rotating cylinder.
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