Lesson 4.2 Objects undergoing uniform circular motion

What is the period (T) in uniform circular motion?

The time taken to complete one revolution. Symbol: T. Unit: second (s). Calculated by: T = time / number of revolutions.

What is the formula for average speed in uniform circular motion and what does each term represent?

v = 2πr/T where v = average speed (m s⁻¹), r = radius of circle (m), T = period (s). The numerator 2πr is the circumference (distance for one revolution).

What is another name for average speed in circular motion and why?

Tangential speed or tangential velocity. From Latin "tangere" meaning "to touch" because the velocity direction is tangent to (touches) the edge of the circle at any point.

What is rotational speed and how does it differ from average speed?

Rotational speed is the number of revolutions an object makes per second (or per minute). Average speed is the linear speed in m s⁻¹. Example: an engine at 750 rpm has a rotational speed but you need radius to find linear speed.

How do you convert rotational speed (rpm) to period (T)?

T = time / number of revolutions. For rpm: T = 60 seconds / rpm. Example: 750 rpm means T = 60/750 = 0.08 s per revolution.

A Gravitron ride has radius 15.0 m and completes 24 turns every minute. Calculate its average speed.

Step 1: Find period T = 60/24 = 2.5 s. Step 2: Use v = 2πr/T = (2 × π × 15.0)/2.5 = 37.7 m s⁻¹ (or 38 m s⁻¹ to 2 s.f.).

What is the study tip for remembering what "average speed" means in circular motion?

For uniform circular motion "average speed" means the linear speed in metres per second (not rotational speed in revolutions per second). The velocity has the same magnitude as speed with direction tangent to the circle.

How do you find revolutions per minute from average speed and radius?

Step 1: Rearrange v = 2πr/T to get T = 2πr/v. Step 2: Calculate revolutions per minute = 60/T. Example: v = 30 m s⁻¹ and r = 90 m gives T = 2π(90)/30 = 18.85 s so rpm = 60/18.85 = 3.2 rpm.

A car travels around a circular track of radius 90.0 m at constant speed 30.0 m s⁻¹. How many revolutions per minute does the driver make?

T = 2πr/v = (2 × π × 90.0)/30.0 = 18.85 s. Revolutions per minute = 60/T = 60/18.85 = 3.2 revolutions per minute (2 s.f.)