A
What is the dot product of two vectors A⃗ and B⃗ if A⃗=(2,3) and B⃗=(4,1)?
11
What is the cross product of A⃗=(1,0,0) and B⃗=(0,1,0)?
(0,0,1)
What is the formula for the centripetal force in uniform circular motion?
Fc= mv2/r or mw2r
What is the angular acceleration if the angular velocity changes from 10 rad/s to 20 rad/s in 5 seconds?
2 rad/s2
What is the torque produced by a force of 10 N applied at a distance of 2 meters from the pivot point?
20 Nm
Find the magnitude of the cross product of A⃗ =(2,3,4) and B⃗ =(1,0,−1).
7.35
What is the relationship between linear velocity and angular velocity in uniform circular motion?
v = rw
How do you calculate the final angular velocity in uniformly accelerated circular motion?
wf = wi + at
The torque is maximized when the force is applied perpendicular to the lever arm.
What is the moment of inertia of a thin rod of length LL and mass mm about an axis perpendicular to the rod and passing through its center?
I=mL2/12
Explain the physical significance of the dot product in terms of work done by a force.
The dot product represents the work done by a force when it moves an object in the direction of the force.
Describe a real-world example where the cross product is used to determine a physical quantity.
An example is calculating the torque produced by a force applied at a point on a lever arm.
What is the equation for angular displacement in uniformly accelerated circular motion?
θ = ωi + ωit + αt2/2
Calculate the moment of inertia of a solid cylinder of mass mm and radius r about its central axis.
I= mr2 / 2
Explain the concept of centripetal force and its direction in uniform circular motion.
Centripetal force is always directed towards the center of the circular path.
How does the dot product change if one of the vectors is multiplied by a scalar?
If A⃗ is multiplied by a scalar k, the dot product becomes k(A⃗⋅B⃗).
Calculate the cross product of A⃗=(3,4,5) and B⃗=(1,2,3).
(2,−4,2)
A car is moving in a circular path with a radius of 50 meters at a constant speed of 20 meters per second. Calculate the centripetal force acting on the car if its mass is 1000 kilograms.
8000 N
A wheel starts from rest and accelerates uniformly at an angular acceleration of 2 rad/s². Calculate the angular velocity of the wheel after 5 seconds.
10 rad/s
You have a balanced scale (balanza) with an object of mass 7 kg at 80 cm from the center and another object of unknown mass at 30 cm from the center on the opposite side. Find the unknown mass of the object.
18.67 Kg
Calculate the cross product of A⃗=(3,4,1) and B⃗=(6,8,2).
(0,0,0)
A particle moves in a circular path of radius 0.3 meters with a constant speed of 15 meters per second. Calculate the centripetal force acting on the particle if its mass is 2 kilograms.
1500 N
A disk starts from rest and accelerates uniformly at an angular acceleration of 4 rad/s². Calculate the angular displacement after 6 seconds.
72 rad
A car starts from rest and accelerates uniformly along a straight path with an acceleration of 3 m/s² for 5 seconds. After this period, the car enters a circular track with a radius of 50 meters and continues to accelerate uniformly at an angular acceleration of 0.5 rad/s². Calculate the centripetal force acting on the car at the end of the 10 seconds on the circular track, given that the mass of the car is 1000 kilograms.
1,404,500 N
A satellite orbits Earth in a circular path with a radius of 7000 kilometers. If the satellite completes one orbit every 90 minutes, calculate its centripetal force acting on it, given that the mass of the satellite is 500 kilograms.
4,730 N