if the angular quantities theta omega and angular acceleration were specified in terms of degrees rather than radians how would the kinematics equations for uniformly accelerated rotational motion have to be altered
To convert angular quantities from radians to degrees, we need to use the conversion factor: 1 radian is equal to 57.3 degrees (approximately).
The kinematics equations for uniformly accelerated rotational motion include:
1. Angular displacement: θ = θ₀ + ω₀t + (1/2)αt²
2. Angular velocity: ω = ω₀ + αt
3. Final angular velocity squared: ω² = ω₀² + 2αθ
4. Time: t = (ω - ω₀) / α
5. Final angular velocity: ω = ω₀ + αt
If the angular quantities (θ, ω, and α) were specified in degrees, we need to convert them to radians before using these equations. To convert degrees to radians, we use the conversion factor: 1 degree is equal to π/180 radians (approximately).
Therefore, to alter the kinematics equations for uniformly accelerated rotational motion:
1. Angular displacement: θ = θ₀ + (ω₀)(π/180)t + (1/2)(α)(π/180)t²
2. Angular velocity: ω = ω₀ + (α)(π/180)t
3. Final angular velocity squared: ω² = ω₀² + 2(α)(π/180)θ
4. Time: t = ((ω - ω₀)(180/π)) / α
5. Final angular velocity: ω = ω₀ + ((α)(180/π))t
By incorporating the conversion factor appropriately, these modified equations can account for angular quantities given in degrees rather than radians.