a. Surface area of Earth: We'll use the formula $( A = 4 $pi r^2 $) where $( r = 6371 $) km: $[ A_{$text{Earth}} = 4 $times 3.14159 $times (6371)^2 $,...
1 Answers 1 viewsa. You wouldn't use an isotope with a half-life similar to that of carbon-14 to determine the age of the Solar System because the timescale involved in the formation of...
1 Answers 1 viewsAngular Motion of a Rod with Beads (a) Instantaneous Angular Velocity at $ t = 5 $ s: We'll differentiate the angular position function with respect to time: \[ \omega = \frac{d\theta}{dt} =...
1 Answers 1 viewsPosition and Linear Acceleration of a Point on a Rotating Wheel (a) Position at $ t = 10 $ s: We'll use the rotational kinematic equation to find the position: \[ \theta =...
1 Answers 1 viewsAngular and Linear Acceleration of a Wind Turbine (a) Angular Acceleration ($ \alpha $): We can calculate the angular acceleration using the formula: \[ \alpha = \frac{\Delta \omega}{\Delta t} \] Given that the turbine...
1 Answers 1 viewsTo calculate the angular speed � ω and linear speed � v of a point on Earth's surface at latitude 3 0 ∘ 30 ∘ North, we can use the following formulas: (a) Angular speed...
1 Answers 1 viewsRotational Rate During a Somersault Dive To find the rotational rate \( \omega \) during the somersault, we use the formula for rotational kinetic energy: \[ K = \frac{1}{2} I \omega^2 \] Where:...
1 Answers 1 viewsRotational Kinetic Energy of a Neutron Star To calculate the rotational kinetic energy \( K \) of the neutron star, we use the formula: \[ K = \frac{1}{2} I \omega^2 \] Where:...
1 Answers 1 viewsGiven: Mass of the disk, \( m_1 = 2.0 \, \text{kg} \) Radius of the disk, \( r_1 = 50 \, \text{cm} = 0.50 \, \text{m} \)...
1 Answers 1 viewsGiven: Radius of the clay cylinder, \( r = 20 \) cm = \( 0.20 \) m Angular velocity, \( \omega = 10 \) rev/s Coefficient of...
1 Answers 1 views