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A particle moves in a circle of radius 2 m with a constant speed of 4 m/s. What is its centripetal acceleration?
2 m/s┬▓
4 m/s┬▓
8 m/s┬▓
16 m/s┬▓
8 m/s┬▓
Centripetal acceleration is the rate of change of tangential velocity in a circular path. For a particle moving with a constant speed v in a circle of radius r, it is calculated using the formula acтАЛ=rv2тАЛ, resulting in 8┬аm/s2.
Centripetal acceleration is the rate of change of tangential velocity in a circular path. For a particle moving with a constant speed v in a circle of radius r, it is calculated using the formula acтАЛ=rv2тАЛ, resulting in 8┬аm/s2.
Think of a car turning a sharp corner; you feel pushed outward because your body wants to go straight, while the centripetal force from the tires keeps the car moving in a circle.
Remember 'AC' for 'Acceleration is Centripetal' calculated by 'v-squared over r'.
acтАЛ=rv2тАЛ тАФ Formula for centripetal acceleration
v=╧Йr тАФ Relationship between linear and angular velocity
Centripetal acceleration is always directed towards the center of the circular path, perpendicular to the velocity vector. Because the direction of motion changes continuously even if speed remains constant, a net force must be acting toward the center, causing this constant centripetal acceleration.
Centripetal acceleration is independent of the mass of the moving object.
The acceleration vector points toward the center of the circle, while the velocity vector is tangent to the circle.
Uniform circular motion implies constant speed but non-zero acceleration due to constant change in direction.
Useful for calculating forces in mechanical systems like gears and turntables.
This formula is only valid for uniform circular motion; non-uniform motion requires tangential acceleration components.
Satellite orbital dynamics
Banking of roads for vehicles
The given speed is 4┬аm/s and radius is 2┬аm. Calculation: acтАЛ=242тАЛ=216тАЛ=8┬аm/s2.
Option A is incorrect as it assumes simple division 4/2. Option B is incorrect as it ignores the squared term. Option D is incorrect as it uses v2 without dividing by r.
C is correct тАФ The centripetal acceleration is calculated using the relation acтАЛ=rv2тАЛ, which yields 8┬аm/s2.
Always verify if the speed is given as linear speed (m/s) or angular velocity (rad/s), as the formula changes to acтАЛ=╧Й2r for angular inputs.
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