An ice puck moving in a straight line
The red arrows represent the velocity vectors of the puck. If the string were cut, the puck would move off in the direction shown by the red vector, as predicted by Newton’s first law.
The applied force (tension) from the string causes the puck to move with uniform circular motion
The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle
When the angle is equal to one radian, the length of the arc (S) is equal to the radius (r) of the circle
Table of common degrees to radians conversions
The change in angle, in radians, of a body as it rotates around a circle
An angle in radians, subtended at the centre of a circle, is the arc length divided by the radius of the circle
The rate of change in angular displacement with respect to time
The angular speed is ω is the rate at which the line AB rotates
Wrap the right hand around the axis of rotation so that the fingers are pointing in the direction of rotation. The thumb points in the direction of the angular velocity vector
The angle Δθ is swept out in a time Δt, but the arc lengths s and S are different and so are the linear speeds
v = rω
Convert the following angular displacement into degrees:
A bird flies in a horizontal circle with an angular speed of 5.25 rad s−1 of radius 650 m.
Calculate:
You will notice your calculator has a degree (Deg) and radians (Rad) modeThis is shown by the “D” or “R” highlighted at the top of the screenRemember to make sure it’s in the right mode when using trigonometric functions (sin, cos, tan) depending on whether the answer is required in degrees or radiansIt is extremely common for students to get the wrong answer (and lose marks) because their calculator is in the wrong mode - make sure this doesn’t happen to you!
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